[CLASS 10] Mathematics MCQs on Pythagoras Theorem

Mathematics Multiple Choice Questions & Answers on “Pythagoras Theorem”.

1. ∆ABC is a right angled triangle, where AB = 5cm, BC = 10cm, AC = 15cm.
a) False
b) True

Answer: a
Clarification: If ∆ABC is a right angled triangle, then it should satisfy the Pythagoras Theorem.
AB = 5cm, BC = 10cm, AC = 15cm
AB² + BC² = 5² + 10² = 25 + 100 = 125
AC² = 15² = 225
Since, AC² ≠ AB² + BC²
Hence, ABC is not a right-angled triangle.

2. What will be the distance of the foot of ladder from the building, if the ladder of 12 m high reaches the top of a building 35 m high from the ground?
a) 32.65 m
b) 32.87 m
c) 31.87 m
d) 32.85 m
Answer: b
3. The heights of two vertical lamp posts are 33 m and 24 m high. If the distance between them is 40 m, then what will be the distance between their tops?
a) 47.89m
b) 56.56m
c) 32.81m
d) 41m
Answer: d

4. ∆ABC is a right-angled triangle, right angled at B and BD ⊥ AC. If BD = 10cm, AB = 5 cm and BC = 5 cm then AC will be?
a) 44.72 cm
b) 5.59 cm
c) 18.11 cm
d) 22.36 cm

Answer: d

5. Which of triangle whose sides are given below are right angled?
a) AB = 89, AC = 80, BC = 39
b) AB = 57, AC = 50, BC = 45
c) AC = 34, AB = 20, BC = 21
d) AC = 50, AB = 32, BC = 20

Answer: a
Clarification: In (a), applying Pythagoras Theorem,
AC² + BC² = 80² + 39² = 7921 = AB²
Hence, this is a right angled triangle.
Now, in (b) applying Pythagoras Theorem,
AC² + BC² = 50² + 45² = 4525 ≠ AB²
Hence, this is not a right angled triangle.
Now, in (c) applying Pythagoras Theorem,
AB² + BC² = 20² + 21² = 841 ≠ AC²
Hence, this is not a right angled triangle.
Now, in (d) applying Pythagoras Theorem,
AB² + BC² = 32² + 20² = 1424 ≠ AC²
Hence, this is not right angled triangle.

6. The lengths of diagonals of a rhombus are 10 cm and 8 cm. What will be the length of the sides of rhombus?
a) 6.40 cm
b) 5.25 cm
c) 2.44 cm
d) 3.29 cm
Answer: a
7. If the side of rhombus is 13 cm and one of its diagonals is 24 cm, then what will be length of the other diagonal?
a) 8.4 cm
b) 4 cm
c) 11 cm
d) 10 cm
Answer: d
8. What will be the length of the altitude of an equilateral triangle whose side is 9 cm?
a) 4.567 cm
b) 7.794 cm
c) 8.765 cm
d) 4.567 cm
Answer: b
9. What will be the length of the square inscribed in a circle of radius 5 cm?
a) 2.34 cm
b) 3.45 cm
c) 5√2 cm
d) 2.45 cm
Answer: c