Q. If the angles of triangle JKL are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
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A.
40 degrees
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B.
60 degrees
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C.
80 degrees
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D.
90 degrees
Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Therefore, 9x = 180, x = 20. The largest angle is 4x = 80 degrees.
Correct Answer: C — 80 degrees
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Q. If the angles of triangle MNO are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
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A.
40 degrees
-
B.
60 degrees
-
C.
80 degrees
-
D.
90 degrees
Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. The largest angle = 4x = 80 degrees.
Correct Answer: C — 80 degrees
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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height of the triangle? (2019)
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A.
6 units
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B.
12 units
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C.
10 units
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D.
8 units
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.
Correct Answer: A — 6 units
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Q. If the area of triangle ABC is 60 square units and the base is 12 units, what is the height? (2019)
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A.
5 units
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B.
10 units
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C.
15 units
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D.
20 units
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height, which gives height = 10 units.
Correct Answer: A — 5 units
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Q. If the sides of triangle DEF are in the ratio 3:4:5, what type of triangle is it? (2021)
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A.
Acute
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B.
Obtuse
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C.
Right
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D.
Equilateral
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer: C — Right
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Q. If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)
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A.
Acute
-
B.
Obtuse
-
C.
Right
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D.
Equilateral
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer: C — Right
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is the measure of angle C? (2021)
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A.
30 degrees
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B.
60 degrees
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C.
90 degrees
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D.
120 degrees
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.
Correct Answer: C — 90 degrees
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the type of triangle? (2020)
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A.
Scalene
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B.
Isosceles
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C.
Equilateral
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D.
Right
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what type of triangle is DEF? (2021)
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A.
Scalene
-
B.
Isosceles
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C.
Equilateral
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D.
Right
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
-
A.
Yes
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B.
No
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C.
Cannot be determined
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D.
Only if angle D is 90 degrees
Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Correct Answer: A — Yes
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Q. In triangle GHI, if angle G = 30 degrees and side GH = 10 cm, what is the length of side HI if angle H = 60 degrees? (2023)
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A.
5 cm
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B.
10 cm
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C.
15 cm
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D.
20 cm
Solution
Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.
Correct Answer: C — 15 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the length of the longest side? (2022)
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A.
10 cm
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B.
24 cm
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C.
26 cm
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D.
Cannot be determined
Solution
The longest side of triangle GHI is GI, which measures 26 cm.
Correct Answer: C — 26 cm
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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter of the triangle? (2022)
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A.
30 cm
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B.
25 cm
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C.
20 cm
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D.
35 cm
Solution
Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.
Correct Answer: A — 30 cm
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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter? (2022)
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A.
30 cm
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B.
25 cm
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C.
20 cm
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D.
15 cm
Solution
Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.
Correct Answer: A — 30 cm
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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the perimeter of the triangle? (2022)
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A.
24 cm
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B.
26 cm
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C.
22 cm
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D.
20 cm
Solution
Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.
Correct Answer: A — 24 cm
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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter? (2022)
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A.
12 cm
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B.
14 cm
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C.
16 cm
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D.
18 cm
Solution
Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.
Correct Answer: B — 14 cm
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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)
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A.
5√2 cm
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B.
10 cm
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C.
10√2 cm
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D.
20 cm
Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.
Correct Answer: A — 5√2 cm
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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)
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A.
1:1
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B.
1:√2
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C.
√2:1
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D.
2:1
Solution
In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.
Correct Answer: A — 1:1
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Q. The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)
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A.
30 cm²
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B.
60 cm²
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C.
24 cm²
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D.
40 cm²
Solution
Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².
Correct Answer: A — 30 cm²
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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)
-
A.
Yes
-
B.
No
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C.
Cannot be determined
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D.
Only if angle A is 90 degrees
Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.
Correct Answer: A — Yes
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Q. The lengths of the sides of triangle GHI are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)
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A.
30 cm²
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B.
60 cm²
-
C.
65 cm²
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D.
78 cm²
Solution
This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².
Correct Answer: A — 30 cm²
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Q. What is the area of an equilateral triangle with a side length of 6 cm? (2022)
-
A.
9√3 cm²
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B.
12√3 cm²
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C.
18√3 cm²
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D.
24√3 cm²
Solution
Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².
Correct Answer: A — 9√3 cm²
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and angle A = 90 degrees? (2023)
-
A.
6 cm
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B.
8 cm
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C.
10 cm
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D.
12 cm
Solution
In a right triangle, the altitude from the right angle to the hypotenuse is equal to the length of the other side. Thus, the altitude is 6 cm.
Correct Answer: A — 6 cm
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Q. What is the relationship between the angles of an equilateral triangle? (2023)
-
A.
All angles are 60 degrees
-
B.
All angles are 90 degrees
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C.
Two angles are equal
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D.
No angles are equal
Solution
In an equilateral triangle, all three angles are equal and measure 60 degrees each.
Correct Answer: A — All angles are 60 degrees
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