Question

The length of a leg of an isosceles right triangle is 20 inches. Find the length of the hypotenuse in radical form

Answer 1

Answer: H = 20$\sqrt{2}$

Step-by-step explanation:

To find the hypotenuse , we will use Pythagoras theorem, which states that

The square of the hypotenuse = the square of the adjacent + the square of the opposite.

Since , we are dealing with isosceles right triangle , this means that :

both the adjacent and the opposite are equal, using the formula to find the hypotenuse , let H represent the hypotenuse , then

$H^{2}$ = $20^{2}$ +  $20^{2}$

$H^{2}$ = 400 + 400

$H^{2}$ = 800

Take the square root of both sides

H = $\sqrt{800}$

$\sqrt{800}$ can be written as $\sqrt{400}$ x$\sqrt{2}$

Therefore :

H = $\sqrt{400}$ x$\sqrt{2}$

H = 20x $\sqrt{2}$

H = 20$\sqrt{2}$