Question

Find the value of x

Answer 1

x = 121

Explanation:

Let the measure of the altitude of the given triangle be h units.

By geometric mean theorem:

`h = √(23 * x) \\ \\ h = √(23x) \\ \\ now \: by \: pythagors \: theorem \\ \\ {(x + 11)}^(2) = {h}^(2) + {x}^(2) \\ \\ \cancel{{x}^(2)} + 22x + 121 = {( √(23x) )}^(2) + \cancel{{x}^(2)} \\ \\ 22x + 121 = 23x \\ \\ 22x - 23x = - 121 \\ \\ - x = - 121 \\ \\ x = 121`