Question

what is the value of x? 12 units 15 units 20 units 24 units

Explanation:

Step1: Apply geometric mean theorem

In a right - triangle \( \triangle SQR\) with altitude \(RT\), we use the geometric mean theorem: \(x^{2}=9\times(9 + 16)\).

Step2: Simplify the right - hand side

First, calculate \(9+16 = 25\). Then \(x^{2}=9\times25\).

Step3: Solve for \(x\)

Since \(x^{2}=225\), taking the square root of both sides (and considering \(x>0\) as it represents a length), we get \(x=\sqrt{225}\).

Answer:

15 units