Question

find the value of x.
note: the figure is not to scale.
the value of x is
(simplify your answer.)

Explanation:

Step1: Apply the geometric mean theorem (altitude-on-hypotenuse theorem)

In a right - triangle, if an altitude is drawn to the hypotenuse, then the length of each segment of the hypotenuse is the geometric mean of the length of the hypotenuse segment adjacent to it and the length of the hypotenuse. Here, we have \((x + 8)^2=x(x + 17)\)
Expanding the left - hand side: \(x^{2}+16x + 64=x^{2}+17x\)

Step2: Solve the equation for \(x\)

Subtract \(x^{2}\) from both sides of the equation:
\(x^{2}-x^{2}+16x + 64=x^{2}-x^{2}+17x\)
\(16x+64 = 17x\)
Subtract \(16x\) from both sides: \(64=17x - 16x\)

Answer:

\(64\)