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
`√(2)`

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 =
`√(800)`

`√(800)` can be written as
`√(400)` x
`√(2)`

Therefore :

H =
`√(400)` x
`√(2)`

H = 20x
`√(2)`

H = 20
`√(2)`