Q. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)
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A.
Equilateral
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B.
Isosceles
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C.
Scalene
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D.
Right-angled
Solution
Since 5² + 12² = 13² (25 + 144 = 169), triangle JKL is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)
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A.
Equilateral
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B.
Isosceles
-
C.
Scalene
-
D.
Right-angled
Solution
Using the Pythagorean theorem, 8² + 15² = 64 + 225 = 289 = 17². Hence, it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)
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A.
120 cm²
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B.
240 cm²
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C.
60 cm²
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D.
80 cm²
Solution
Using Heron's formula, s = (10 + 24 + 26) / 2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = √(4800) = 120 cm².
Correct Answer:
A
— 120 cm²
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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 PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter of the triangle? (2022)
-
A.
12 cm
-
B.
14 cm
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C.
16 cm
-
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 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 45-45-90, the sides opposite the equal angles are equal, hence the ratio is 1:1.
Correct Answer:
A
— 1:1
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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
-
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. In triangle XYZ, if XY = 12 cm, YZ = 16 cm, and XZ = 20 cm, what is the semi-perimeter? (2020)
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A.
24 cm
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B.
28 cm
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C.
30 cm
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D.
32 cm
Solution
Semi-perimeter s = (XY + YZ + XZ)/2 = (12 + 16 + 20)/2 = 24 cm.
Correct Answer:
A
— 24 cm
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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, what is the length of the longest side? (2020)
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A.
8 cm
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B.
15 cm
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C.
17 cm
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D.
Not determinable
Solution
The longest side in triangle XYZ is XZ, which measures 17 cm.
Correct Answer:
C
— 17 cm
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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
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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
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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. The perimeter of an equilateral triangle is 36 cm. What is the length of each side? (2021)
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A.
9 cm
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B.
12 cm
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C.
10 cm
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D.
8 cm
Solution
In an equilateral triangle, all sides are equal. Therefore, each side = Perimeter / 3 = 36 / 3 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. What is the area of an equilateral triangle with a side length of 6 cm? (2022)
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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)
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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 length of the altitude from vertex A to side BC in triangle ABC, where AB = 5 cm, AC = 12 cm, and BC = 13 cm? (2023)
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A.
5 cm
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B.
6 cm
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C.
7 cm
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D.
8 cm
Solution
Using Heron's formula, the area is 30 cm². The altitude = (2 * Area) / base = (2 * 30) / 13 = 6 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the median from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and BC = 8 cm? (2023)
-
A.
5 cm
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B.
6 cm
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C.
7 cm
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D.
8 cm
Solution
Using the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a = BC, b = AC, c = AB. m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2) = 7 cm.
Correct Answer:
C
— 7 cm
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Q. What is the perimeter of an equilateral triangle with each side measuring 8 cm? (2021)
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A.
16 cm
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B.
24 cm
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C.
32 cm
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D.
20 cm
Solution
The perimeter of an equilateral triangle is 3 times the length of one side. Therefore, perimeter = 3 * 8 = 24 cm.
Correct Answer:
B
— 24 cm
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Q. What is the relationship between the angles of an equilateral triangle? (2023)
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A.
All angles are 60 degrees
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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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Q. What is the sum of the interior angles of a triangle? (2019)
-
A.
90 degrees
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B.
180 degrees
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C.
270 degrees
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D.
360 degrees
Solution
The sum of the interior angles of any triangle is always 180 degrees.
Correct Answer:
B
— 180 degrees
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