Q. If the angles of triangle JKL are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
90 degrees
Show solution
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)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
90 degrees
Show solution
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 AC is 12 units, what is the height from point B to line AC? (2019)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
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 area of triangle ABC is 60 square units and the base is 10 units, what is the height of the triangle? (2019)
A.
6 units
B.
12 units
C.
10 units
D.
8 units
Show solution
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 10 units, what is the height? (2019)
A.
6 units
B.
12 units
C.
10 units
D.
8 units
Show solution
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)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
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 area of triangle ABC is 60 square units and the base is 12 units, what is the height of the triangle? (2019)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
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 base of a triangle is 10 cm and the height is 5 cm, what is the area of the triangle? (2022)
A.
25 cm²
B.
50 cm²
C.
15 cm²
D.
30 cm²
Show solution
Solution
Area = (1/2) * base * height = (1/2) * 10 * 5 = 25 cm².
Correct Answer:
A
— 25 cm²
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Q. If the perimeter of triangle DEF is 36 cm and the lengths of sides DE and EF are 10 cm and 12 cm respectively, what is the length of side DF? (2020)
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Perimeter = DE + EF + DF. Therefore, DF = 36 - (10 + 12) = 14 cm.
Correct Answer:
C
— 14 cm
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Q. If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, hence it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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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)
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
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)
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
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 AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)
A.
70 degrees
B.
80 degrees
C.
60 degrees
D.
50 degrees
Show solution
Solution
In an isosceles triangle, angles opposite to equal sides are equal. Therefore, angle B = angle C = (180 - 40) / 2 = 70 degrees.
Correct Answer:
B
— 80 degrees
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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)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
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 length of side DE if DF = 10 cm? (2023)
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
20 cm
Show solution
Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. DE = DF/√2 = 10/√2 = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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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)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
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)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
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 = 12 cm, EF = 16 cm, and DF = 20 cm, what is the semi-perimeter? (2021)
A.
24 cm
B.
28 cm
C.
30 cm
D.
20 cm
Show solution
Solution
Semi-perimeter s = (12 + 16 + 20) / 2 = 48 / 2 = 24 cm.
Correct Answer:
B
— 28 cm
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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
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
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)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
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 angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)
A.
15 cm
B.
10 cm
C.
12 cm
D.
9 cm
Show solution
Solution
Using the Pythagorean theorem, GI = √(HI² - GH²) = √(12² - 9²) = √(144 - 81) = √63 = 15 cm.
Correct Answer:
A
— 15 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)
A.
120 cm²
B.
130 cm²
C.
140 cm²
D.
150 cm²
Show solution
Solution
Using Heron's formula, semi-perimeter s = (10 + 24 + 26) / 2 = 30. Area = √(s(s-a)(s-b)(s-c)) = √(30*20*6*4) = 120 cm².
Correct Answer:
A
— 120 cm²
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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)
A.
10 cm
B.
24 cm
C.
26 cm
D.
Cannot be determined
Show solution
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 GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the perimeter? (2019)
A.
50 cm
B.
60 cm
C.
70 cm
D.
80 cm
Show solution
Solution
Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.
Correct Answer:
A
— 50 cm
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Q. In triangle GHI, if the lengths of sides GH, HI, and GI are in the ratio 3:4:5, what type of triangle is it? (2019)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of JL? (2022)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
Show solution
Solution
Using the Pythagorean theorem, JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12.25 cm.
Correct Answer:
B
— 12 cm
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
Show solution
Solution
Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.
Correct Answer:
B
— 12 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)
A.
30 cm
B.
25 cm
C.
20 cm
D.
15 cm
Show solution
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 of the triangle? (2022)
A.
30 cm
B.
25 cm
C.
20 cm
D.
35 cm
Show solution
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 type of triangle? (2023)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.
Correct Answer:
D
— Right-angled
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