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In a triangle, the sum of squares of two sides is equal to the square of the third side. State whether the statement is true or false.

Solution:

Given, the sum of squares of two sides is equal to the square of the third side in a triangle.

We have to determine if the given statement is true or false.

(i) consider the sides of the triangle as 2 cm, 3 cm and 4 cm.

According to the question,

Sum of squares of two sides = 2² + 3²

= 4 + 9

= 13 cm

Square of third side = 4² = 16 cm

So, 13 ≠ 16

(ii) consider a right triangle with sides 3 cm, 4 cm and 5 cm.

Sum of squares of two sides = 3² + 4²

= 9 + 16

= 25 cm

Square of third side = 5² = 25 cm

So, 25 = 25

Therefore, only in a right angled triangle the sum of squares of two sides is equal to the third side.

✦ Try This: In a triangle, the sum of cubes of two sides is equal to the cube of the third side. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 70

Summary:

The given statement,”In a triangle, the sum of squares of two sides is equal to the square of the third side” is false.

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