Questions
Q1. Which of the following lengths cannot form a right-angled triangle?
(a) 5 units, 12 units, 13 units
(b) 24 units, 10 units, 26 units
(c) 8 units, 6 units, 10 units
(d) 17 units, 5 units, 22 units
Q2. A triangle having an angle 90° and a pair of equal sides will have other two angles equal to:
(a) 30°
(b) 60°
(c) 45°
(d) 180°
Q3. Which of the following sets of lengths cannot form a right-angled triangle?
(a) 7 units, 24 units, 25 units
(b) 9 units, 12 units, 15 units
(c) 10 units, 6 units, 8 units
(d) 11 units, 6 units, 18 units
Q4. Which of the following sets of lengths can form a right-angled triangle?
(a) 8 units, 15 units, 17 units
(b) 5 units, 7 units, 11 units
(c) 9 units, 12 units, 16 units
(d) 6 units, 10 units, 13 units
Q5. A right-angled triangle has a pair of equal sides. The measures of the other two angles are:
(a) 30° and 60°
(b) 45° and 45°
(c) 60° and 60°
(d) 90° and 45°
Q6. The sides of a triangle are in the ratio 3:4:5. The triangle is:
(a) Equilateral
(b) Isosceles
(c) Right-angled
(d) Obtuse-angled
Q7. If one angle of a triangle is 90° and the other two angles are equal, what type of triangle is it?
(a) Isosceles right triangle
(b) Scalene right triangle
(c) Equilateral triangle
(d) Obtuse triangle
Q8. Which of the following cannot be the sides of a triangle?
(a) 3, 4, 5
(b) 7, 10, 18
(c) 5, 12, 13
(d) 6, 8, 10
Q9. A triangle with sides 9 units, 40 units, 41 units is:
(a) Right-angled
(b) Isosceles
(c) Equilateral
(d) Acute-angled
Q10. Which of the following sets of lengths cannot form a right-angled triangle?
(a) 6 units, 8 units, 10 units
(b) 5 units, 12 units, 13 units
(c) 7 units, 24 units, 25 units
(d) 9 units, 15 units, 20 units
Q11. Which of the following sets of lengths can form a right-angled triangle?
(a) 12 units, 16 units, 20 units
(b) 8 units, 10 units, 19 units
(c) 9 units, 14 units, 22 units
(d) 15 units, 20 units, 30 units
Q12. A triangle has a 90° angle and two equal sides. The measures of the other two angles are:
(a) 30° and 60°
(b) 45° and 45°
(c) 60° and 60°
(d) 50° and 40°
Q13. The sides of a triangle are in the ratio 5:12:13. The triangle is:
(a) Equilateral
(b) Isosceles
(c) Right-angled
(d) Obtuse-angled
Q14. If one angle of a triangle is 90° and the other two angles are equal, what type of triangle is it?
(a) Isosceles right triangle
(b) Scalene right triangle
(c) Equilateral triangle
(d) Obtuse triangle
Q15. Which of the following cannot be the sides of any triangle?
(a) 4, 5, 6
(b) 7, 2, 10
(c) 8, 15, 17
(d) 6, 8, 10
Q16. A triangle with sides 10 units, 24 units, 26 units is:
(a) Right-angled
(b) Isosceles
(c) Equilateral
(d) Acute-angled
Q17. The hypotenuse of a right-angled triangle is 13 units. One side is 5 units. Find the other side.
(a) 10 units
(b) 12 units
(c) 8 units
(d) 11 units
Q18. A triangle has angles in the ratio 1:1:2. Its type is:
(a) Equilateral
(b) Isosceles
(c) Right-angled
(d) Obtuse
Q19. A triangle has sides 7 units, 24 units, and 25 units. Its largest angle is:
(a) 60°
(b) 90°
(c) 75°
(d) 45°
Answer Key with Explanations
Q1 → (d)
- Use Pythagoras theorem: 172=52+222 → cannot form a right-angled triangle.
Q2 → (c)
- Right-angled triangle with equal sides → other two angles = 45° each.
Q3 → (d)
- Check each set using a2+b2=c2. 11, 6, 18 fails.
Q4 → (a)
- Only 8, 15, 17 satisfies Pythagoras theorem.
Q5 → (b)
- Isosceles right triangle → angles 45°, 45°, 90°.
Q6 → (c)
- 3² + 4² = 5² → Right-angled triangle.
Q7 → (a)
- Two equal angles + one 90° → Isosceles right triangle.
Q8 → (b)
- Triangle inequality: 7 + 10 > 18 ❌ fails.
Q9 → (a)
- 9² + 40² = 41² → Right-angled triangle.
Q10 → (d)
- 9² + 15² ≠ 20² → cannot form right-angled triangle.
Q11 → (a)
- 12² + 16² = 20² → Right-angled triangle.
Q12 → (b)
- Right-angled triangle with equal sides → angles 45° and 45°.
Q13 → (c)
- 5² + 12² = 13² → Right-angled triangle.
Q14 → (a)
- Right-angled with other two angles equal → Isosceles right triangle.
Q15 → (b)
- Triangle inequality: 7 + 2 < 10 → cannot form triangle.
Q16 → (a)
- 10² + 24² = 26² → Right-angled triangle.
Q17 → (b)
- Use Pythagoras: 132−52=169−25=144, √144 = 12
Q18 → (b)
- Angles = 45°, 45°, 90° → Isosceles right triangle.
Q19 → (b)
- Largest side = 25 → opposite angle = 90° → Right-angled triangle.
