Question

Find the unknown side length x write your answer in simplest radical form

A.24
B.4squareroot37
C.2squareroot154
D.5squareroot117

Answer 1

(B)
`4√(37)`

Explanation:

First, we determine the height of the triangle which we label as y.

Using Pythagoras Theorem.

`25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=√(576)\\y=24`

In the smaller right triangle with hypotenuse, x

Base = 7-3 =4 Units

Height, y= 24 Units

Therefore, applying Pythagoras Theorem.:

`x^2=24^2+4^2\\x^2=592\\x=√(592)\\ x=4√(37)`