Question

i \can\ similarity solve for x. triangle with right angle, altitude to hypotenuse, side 15, segment 9, x as hypotenuse a 16 b 18 c 25 d 24

Explanation:

Step1: Use geometric mean theorem

In a right - triangle, if an altitude is drawn from the right angle to the hypotenuse, then the length of the hypotenuse \(x\) and the segments of the hypotenuse satisfy the relationship: if one segment is \(a = 9\) and the adjacent side to the segment is \(b=15\), then \(b^{2}=a\times x\).
So, \(15^{2}=9\times x\).

Step2: Solve for \(x\)

We have the equation \(225 = 9x\).
Dividing both sides by \(9\), we get \(x=\frac{225}{9}\).

Answer:

\(x = 25\), so the answer is C. 25