Question

In a right angle triangle, if the sum of the squares of the sides a right angle is 169, then what is the length of hypotenuse​

Answer 1

In right angled ∆

by Pythagoras theorem

hypotenuse square = sum of side square

hypotenuse square = 169 ( given)

taking square root both side

hypotenuse = √169

hypotenuse = 13

Answer 2

Given :

• In a right angle triangle, the sum of the squares of the sides is 169

To find :

• The length of the hypotenuse.

Solution :

Let ABC be the right angle triangle.

Thus,

(AB)² + (BC)² = 169⠀⠀⠀⠀⠀ [given]

Hence,

We know that,

(AB)² + (BC)² = (AC)²

i.e.

Sum of squares of sides = Hypotenuse side

[By Pythagorean triplet]

So,

→ 169 = (AC)²

→ AC = √169

→ AC = √13 × 13

→ AC = 13 cm

Therefore,

• The length of the hypotenuse is 13 cm respectively.