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CBSE Class 10  >  Class 10 Test  >  Online MCQ Tests  >  Test: Pythagoras Theorem - Class 10 MCQ

Pythagoras Theorem - Free MCQ Practice Test with solutions, Class 10


MCQ Practice Test & Solutions: Test: Pythagoras Theorem (15 Questions)

You can prepare effectively for Class 10 Online MCQ Tests for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Pythagoras Theorem". These 15 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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Test: Pythagoras Theorem - Question 1
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Which of the following cannot be the sides a right triangle?​

Detailed Solution: Question 1

H2 = P2 + B2
H2 = 81
P2 + B2 = 25 + 49 = 74
H2  ≠ P2+B2.Therefore the sides cannot form a right triangle.

Test: Pythagoras Theorem - Question 2
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In a triangle ABC, AC= √180, AB = 6, BC = 12. What is ∠B = ?

Detailed Solution: Question 2

We have AB2=36 and BC2=144
Adding both the squares we get 
AB2+BC2=36+144=180
=AC2
So , AC is the hypotenuse according to pythagoras theorem , So the angle opposite to it which is B is 90 degrees.

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Test: Pythagoras Theorem - Question 3
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From the given figure, find the unknown x.

​

Detailed Solution: Question 3

Since the triangle is a right angled triangle,
Applying Pythagoras Theorem,
H2=P2+B2
152=P2+92
P2=225-81=144
P=12

Test: Pythagoras Theorem - Question 4
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Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?​

Test: Pythagoras Theorem - Question 5
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What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm?

Detailed Solution: Question 5

We have a TV which is a rectangle whose adjacent sides form an angle of 90 degrees so The triangle formed by the two sides and a diagonal will be a right angle. So, Applying Pythagoras Theorem,
(Diagonal)2=802+602=6400+3600=10000
Diagonal=100cm

Test: Pythagoras Theorem - Question 6
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Which of the following is a Pythagorean triplet ?​

Detailed Solution: Question 6

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².

a) 432 = 1849

   362+182 = 1620

b) 252  = 625

    152 + 202 =625

c) 132 = 169

    32 + 122 = 153

d) 262 = 676

    242 + 252 = 1201

so option b is correct

Test: Pythagoras Theorem - Question 7
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QM ⊥ RP and PR2 – PQ2 = OR2. If∠QPM = 30°, Then ∠MQR is

​

Detailed Solution: Question 7

In triangle PMQ
Angle M = 90°
Angle P = 30°
Angle QMP + Angle MPQ + Angle PQM = 180 degree ( By angle sum property )
90 + 30 + Angle PQM = 180
Angle PQM = 180 - 120
Angle PWM = 60 Degree
QM divides Angle PQR into two equal parts .
Therefore Angle MQR = 30°

Test: Pythagoras Theorem - Question 8
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In the above figure, AB = c, BC = a, AC = b, AD = y, DB = p. Check which of the following options is correct ?​

Test: Pythagoras Theorem - Question 9
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In right triangled ABC right angled at B, a line DE is drawn through the mid point D of AB and parallel to BC. If AB = 9 cm, BC = 12 cm. AE = ?​

Detailed Solution: Question 9

In a triangle ABC in which angle B = 90 degree
So, AB is height of the given triangle = 9 cm
Base of triangle i.e, BC = 12 cm
DE is || to BC
D is the mid point of side AB and E is the mid point of side AC
By applying pythagoras
AC2 = AB2 + BC2
AC2 = 9^2 + 12^2
AC2 = 81 + 144
AC2 = 225
AC = root under 225
AC = 15 cm
E is the mid point of AC
Therefore AE = AC / 2
AE = 15 / 2
AE = 7.5 cm

Test: Pythagoras Theorem - Question 10
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A boy is trying to catch fish sitting at a height of 12 m from the surface of the water. A big fish is at a horizontal distance of 5 m from him. What should be the length of his string to get the fish?

Test: Pythagoras Theorem - Question 11
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Three numbers form a Pythagorean triplet. Two of them are 15 and 17 where 17 is the largest of them. The third number is

Test: Pythagoras Theorem - Question 12
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Triangle PQR is an isosceles right triangle right angled at Q. If PR = √50. What is the value of each of the equal sides?​

Test: Pythagoras Theorem - Question 13
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The length of an altitude of an equilateral triangle of side a is:

Test: Pythagoras Theorem - Question 14
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Two friends A and B start from the same point in the Eastern and Northern directions at the same time. How far are they from each other when A has travelled 5 km and B has travelled 12 km. distance?​

Test: Pythagoras Theorem - Question 15
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Two similar right triangles ABC and PQR are as shown in the figure.If AB = √3 , PQ = √3/2,BC = 1. Find PR = ?

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About this Class 10 Practice Test

This test contains 15 MCQs on Pythagoras Theorem with detailed solutions for each question. It is part of the Online MCQ Tests for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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