Question

What is the measure of x?ztХ.ГУ49x = [?]=Give your answer in simplest form.Enter

Answer 1

Step-by-step 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:

`\frac{\text{Shorter leg in Triangle 1}}{\text{Shorter leg in Triangle 2}}=\frac{\text{hypotenuse in Triangle 1}}{\text{hypotenuse in Triangle 2}}`

We plug in what we know:

`\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}} \\ (4)/(x)=(x)/(13) \\ \text{Simplify and rearrange} \\ (x)(x)=(4)(13) \\ x^2=52 \\ x=\sqrt[]{52} \\ x=2\sqrt[]{13} \end{gathered}`

Therefore, the answer is:

`x=2\sqrt[]{13}`