# How to Find the Hypotenuse of a Right Triangle

Find the length of the hypotenuse of a triangle which is extended from the side of another right triangle

APQ is a triangle with sides 3 cm,4 cm and 5 cm

Extend AP and draw a perpendicular line to AB which is passing through B and form another triangle ABQ

Then find the length of AB

## Solution

Let PC = *x*

## From figure hypotenuse of the triangle = **PA + PC = 3 +*** x*

*x*

Apply Pythagoras theorem in triangle APB

BC² = AC² – AB² = (3 + *x*)² – 5²……………….eq(1)

Apply Pythagoras theorem in triangle BPC

BC² = BP² + PC² = 4² – *x*²……………………..eq(2)

(3 + *x*)² – 5² = 4² – *x*²

⇒ 9 + 6x + x² – 25 = 16 + *x*²

⇒ 6*x* = 32

⇒ *x* = 16/3 cm

So, **Hypotenuse of the right triangle** = 3 + 16/3 = **25/3 cm**