Answer:
Explanation:
We can notice that the triangles formed are similar to the original triangle since an altitude is drawn from the right angle.
To find the measure of x, we use ratio:
Triangle 1:
Triangle 2:
So, we use the formula:
[tex]\frac{\text{Shorter leg in Triangle 1}}{\text{Shorter leg in Triangle 2}}=\frac{\text{hypotenuse in Triangle 1}}{\text{hypotenuse in Triangle 2}}[/tex]
We plug in what we know:
[tex]\begin{gathered} \frac{\text{Shorter leg in Triangle 1}}{\text{Shorter leg in Triangle 2}}=\frac{\text{hypotenuse in Triangle 1}}{\text{hypotenuse in Triangle 2}} \\ \frac{4}{x}=\frac{x}{13} \\ \text{Simplify and rearrange} \\ (x)(x)=(4)(13) \\ x^2=52 \\ x=\sqrt[]{52} \\ x=2\sqrt[]{13} \end{gathered}[/tex]
Therefore, the answer is:
[tex]x=2\sqrt[]{13}[/tex]
