Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?
Solution
Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer: B — 5
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Q. In triangle ABC, if the lengths of sides a = 10, b = 24, and angle C = 60 degrees, find the length of side c.
Solution
Using the cosine rule: c^2 = a^2 + b^2 - 2ab*cos(C) = 10^2 + 24^2 - 2*10*24*(1/2) = 100 + 576 - 240 = 436. Thus, c = √436 = 20.
Correct Answer: A — 20
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Q. In triangle ABC, if the lengths of sides a, b, and c are 5, 12, and 13 respectively, what is the perimeter of the triangle?
Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?
-
A.
84
-
B.
96
-
C.
120
-
D.
168
Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer: B — 96
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Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Isosceles
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?
Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?
-
A.
30 cm
-
B.
40 cm
-
C.
50 cm
-
D.
60 cm
Solution
Perimeter = 8 + 15 + 17 = 40 cm.
Correct Answer: A — 30 cm
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?
-
A.
60
-
B.
80
-
C.
120
-
D.
150
Solution
Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.
Correct Answer: A — 60
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are a = 5, b = 12, and c = 13, what is the perimeter of the triangle?
Solution
The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?
-
A.
0.5
-
B.
0.6
-
C.
0.8
-
D.
0.9
Solution
Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.
Correct Answer: C — 0.8
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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the perimeter?
Solution
The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.
Correct Answer: A — 30
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Q. In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Right
-
D.
Scalene
Solution
The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
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 MNO, if angle M = 45 degrees and angle N = 45 degrees, what is angle O?
-
A.
90 degrees
-
B.
45 degrees
-
C.
60 degrees
-
D.
30 degrees
Solution
Angle O = 180 - (angle M + angle N) = 180 - (45 + 45) = 90 degrees.
Correct Answer: A — 90 degrees
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Q. In triangle PQR, if PQ = 10 cm, QR = 24 cm, and PR = 26 cm, what is the area of the triangle?
-
A.
120 cm²
-
B.
120√3 cm²
-
C.
240 cm²
-
D.
48 cm²
Solution
Using Heron's formula, s = (10 + 24 + 26)/2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = 120 cm².
Correct Answer: A — 120 cm²
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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
D.
Only if XY is the hypotenuse
Solution
Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.
Correct Answer: A — Yes
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Q. The area of triangle ABC is 24 cm², and the base BC = 8 cm. What is the height from A to BC?
-
A.
6 cm
-
B.
8 cm
-
C.
4 cm
-
D.
3 cm
Solution
Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.
Correct Answer: A — 6 cm
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Q. The area of triangle ABC is 30 square units, and the base BC is 10 units. What is the height from A to BC?
-
A.
3 units
-
B.
6 units
-
C.
5 units
-
D.
4 units
Solution
Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.
Correct Answer: B — 6 units
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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. What is the area of an equilateral triangle with side length 'a'?
-
A.
(√3/4)a²
-
B.
(1/2)a²
-
C.
(√2/2)a²
-
D.
(3/2)a²
Solution
The area of an equilateral triangle is given by the formula (√3/4)a².
Correct Answer: A — (√3/4)a²
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Q. What is the circumradius of a triangle with sides 5, 12, and 13?
Solution
For a right triangle, the circumradius R = hypotenuse/2 = 13/2 = 6.5.
Correct Answer: B — 7
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Q. What is the circumradius of a triangle with sides 6, 8, and 10?
Solution
Circumradius R = (abc)/(4K), where K is the area. Area K = 24 (using Heron's formula). R = (6*8*10)/(4*24) = 5.
Correct Answer: A — 5
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Q. What is the circumradius of a triangle with sides 7, 24, and 25?
-
A.
12.5
-
B.
13
-
C.
14
-
D.
15
Solution
The circumradius R of a triangle can be calculated using the formula R = (abc)/(4 * Area). Here, Area = 84 cm², so R = (7 * 24 * 25)/(4 * 84) = 13.
Correct Answer: B — 13
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Q. What is the circumradius of an equilateral triangle with side length a?
-
A.
a/√3
-
B.
a/2
-
C.
a/√2
-
D.
a/√3
Solution
The circumradius R of an equilateral triangle is given by R = a/(√3).
Correct Answer: D — a/√3
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