In a right angled triangle, the square of hypotenuse is equal to the sum of the square of other two sides.

Right angle \(\triangle ABC\)

In the above right angle \(\triangle ABC\), p is perpendicular, b is base and h is hypotenuse.

\(h^2 = b^2 + p^2\)

or \(h = \sqrt{b^2 + p^2}\)

Example

**
Find the length of hypotenuse of right angle \(\triangle ABC\), where length of base =3cm and length of perpendicular = 9cm.
**

**Solution:**

In \(\triangle ABC\)

b=3cm

p=4cm

\(\because \), \(\triangle ABC\) is a right angle triangle (given)

\(\therefore \) by applying Pythagoras theorem

\(h = \sqrt{b^2 + p^2}\)

\(h = \sqrt{3^2 + 4^2}\)

\(h = \sqrt{9 + 16}\)

\(h = \sqrt{25}\)

\(\therefore \) \(h = 5cm\)