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This contains 15 Multiple Choice Questions for Class 10 Test: Pythagoras Theorem (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which of the following cannot be the sides a right triangle?

Solution:

H^{2 }= P^{2 }+ B^{2}

H^{2} = 81

P^{2 }+ B^{2 }= 25 + 49 = 74

H^{2 } ≠ P^{2}+B^{2}.Therefore the sides cannot form a right triangle.

QUESTION: 2

In a triangle ABC, AC= √180, AB = 6, BC = 12. What is ∠B = ?

Solution:

We have AB^{2}=36 and BC^{2}=144

Adding both the squares we get

AB^{2}+BC^{2}=36+144=180

=AC^{2}

So , AC is the hypotenuse according to pythagoras theorem , So the angle opposite to it which is B is 90 degrees.

QUESTION: 3

From the given figure, find the unknown x.

Solution:

Since the triangle is a right angled triangle,

Applying Pythagoras Theorem,

H^{2}=P^{2}+B^{2}

15^{2}=P^{2}+9^{2}

P^{2}=225-81=144

P=12

QUESTION: 4

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?

Solution:

QUESTION: 5

What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm?

Solution:

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}=80^{2}+60^{2}=6400+3600=10000

Diagonal=100cm

QUESTION: 6

Which of the following is a Pythagorean triplet ?

Solution:

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

a) 43^{2} = 1849

36^{2}+18^{2} = 1620

b) 25^{2 }= 625

15^{2 }+ 20^{2} =625

c) 13^{2} = 169

3^{2} + 12^{2} = 153

d) 26^{2} = 676

24^{2} + 25^{2} = 1201

so option b is correct

QUESTION: 7

QM ⊥ RP and PR^{2} – PQ^{2} = OR^{2}. If∠QPM = 30°, Then ∠MQR is

Solution:

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°

QUESTION: 8

In the above figure, AB = c, BC = a, AC = b, AD = y, DB = p. Check which of the following options is correct ?

Solution:

QUESTION: 9

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 = ?

Solution:

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

AC^{2} = AB^{2} + BC^{2}

AC^{2} = 9^2 + 12^2

AC^{2} = 81 + 144

AC^{2} = 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

QUESTION: 10

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?

Solution:

QUESTION: 11

Three numbers form a Pythagorean triplet. Two of them are 15 and 17 where 17 is the largest of them. The third number is

Solution:

QUESTION: 12

Triangle PQR is an isosceles right triangle right angled at Q. If PR = √50. What is the value of each of the equal sides?

Solution:

QUESTION: 13

The length of an altitude of an equilateral triangle of side a is:

Solution:

QUESTION: 14

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?

Solution:

QUESTION: 15

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

Solution:

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