Question

Find the value of x

Answer 1

Answer:

x = 121

Step-by-step explanation:

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

By geometric mean theorem:

$h = \sqrt{23 \times x} \\ \\ h = \sqrt{23x} \\ \\ now \: by \: pythagors \: theorem \\ \\ {(x + 11)}^{2} = {h}^{2} + {x}^{2} \\ \\ \cancel{{x}^{2}} + 22x + 121 = {( \sqrt{23x} )}^{2} + \cancel{{x}^{2}} \\ \\ 22x + 121 = 23x \\ \\ 22x - 23x = - 121 \\ \\ - x = - 121 \\ \\ x = 121$