Question

question 5 (1 point)
find the value of x.
(image of a right triangle with a perpendicular segment to the hypotenuse, hypotenuse segments 16 and 9, and leg x)
blank 1:

Explanation:

Step1: Recall Geometric Mean Theorem

In a right triangle, the length of a leg is the geometric mean of the length of the hypotenuse segment adjacent to that leg and the length of the entire hypotenuse. The hypotenuse here is \(16 + 9=25\), and the segment adjacent to \(x\) is \(9\), the entire hypotenuse is \(25\). So by the theorem, \(x^{2}=9\times25\).

Step2: Solve for \(x\)

Calculate \(9\times25 = 225\), then take the square root of both sides: \(x=\sqrt{225}=15\).

Answer:

15