Question

use the geometric mean to solve for the value of x. round your answer to the nearest tenth.
(1 point)
x =\square

Explanation:

Step1: Recall geometric mean in right triangles

In a right triangle, when an altitude is drawn to the hypotenuse, the length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse. Here, the two segments of the hypotenuse are \( 13 \) and \( 4 \), and \( x \) is the altitude. So, the formula is \( x = \sqrt{13\times4} \).

Step2: Calculate the product inside the square root

First, calculate \( 13\times4 = 52 \).

Step3: Take the square root and round

Now, find the square root of \( 52 \). \( \sqrt{52} \approx 7.2111 \). Rounding to the nearest tenth gives \( 7.2 \).

Answer:

\( 7.2 \)