Question

solve for x.

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if the altitude drawn to the hypotenuse is \(h\), and the segments of the hypotenuse are \(a\) and \(b\), then \(h^{2}=a\times b\). Let the two segments of the hypotenuse be \(m\) and \(n\) such that \(x=m + n\), and \(h = 48\), one segment \(n = 64\). Let the other segment be \(m\). We know that \(48^{2}=m\times64\).

Step2: Solve for \(m\)

\[

$$\begin{align*} m&=\frac{48^{2}}{64}\\ m&=\frac{2304}{64}\\ m& = 36 \end{align*}$$

\]

Step3: Calculate \(x\)

Since \(x=m + 64\), substituting \(m = 36\) into the equation, we get \(x=36+64\).
\[x = 100\]

Answer:

100