Question

The lengths of two sides of a right triangle are equal. The square of the hypotenuse is 450cm².Then length of each equal side is

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

Length of two sides of right triangle are equal.

Hypotenuse is $450 {cm}^{2}$

To Find :

Length of each side

We know that Right Triangle is the triangle which having one $90^{\circ}$angle.

=>If any two sides are equal then their angles are also equal.

According to the Question if two sides are equal.

Then,let us assume that the first side be 'x' which is equal to the second side e.g ,'x'

Now ,by Pythagoras theorem

$\boxed{\sf{H}^{2} = {P}^{2} + {B}^{2}}$

Where,H is hypotenuse ,P is perpendicular and B is its base

$\sf = > {x}^{2} + {x}^{2} = 450 {cm}^{2}$

$\sf= > 2 {x}^{2} = 450$

$\sf = > {x}^{2} = 225$

$\sf = > x = \sqrt{225} = 15$

$\therefore$ The length of two sides is 15 cm each.

Check :

$\sf= > {H}^{2} = {P}^{2} + {B}^{2}$

$\sf450 {cm}^{2} = {(15)}^{2} + {(15)}^{2}$

$\sf= 225 + 225 = 450 {cm}^{2}$