Question

A right triangle has legs of length 4x and 20x. What is an expression for the hypotenuse of the right triangle

Answer 1

`4x√(26)`.

Explanation:

Given information:

`Leg_1=4x`

`Leg_2=20x`

According to the Pythagoras theorem,

`(hypotenuse)^2=(Leg_1)^2+(leg_2)^2`

Using Pythagoras theorem, we get

`(hypotenuse)^2=(4x)^2+(20x)^2`

`(hypotenuse)^2=16x^2+400x^2`

`(hypotenuse)^2=416x^2`

Taking square root on both sides.

`hypotenuse=√(416x^2)`

`hypotenuse=4x√(26)`

Hence, the expression of the hypotenuse is
`4x√(26)`.