Question

Geometry: Find the value of X

Answer 1

`x = √(30)`

Explanation:

BD is the altitude of the right ∆ which divides the hypotenuse to create two line segments, CD, and AD.

According to the right triangle altitude theorem,

`BD = √(CD*AD)`

CD = 3, AD = 7, therefore,

`BD = √(3*7)`

`BD = √(21)`

Find x using Pythagorean theorem

`x^2 = BD^2 + CD^2`

`x^2 = (√(21))^2 + 3^2`

`x^2 = 21 + 9`

`x^2 = 30`

`x = √(30)`