Question

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

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 \( SQ = ST + TQ = 9 + 16 = 25 \). For leg \( RQ = x \), adjacent segment \( TQ = 16 \), so \( x^2 = TQ\times SQ \).

Step2: Substitute values and solve

Substitute \( TQ = 16 \) and \( SQ = 25 \) into the formula: \( x^2 = 16\times25 \). Calculate \( 16\times25 = 400 \), then \( x=\sqrt{400}=20 \).

Answer:

20 units