Question

find the value of x.
note: the figure is not to scale.
the value of x is
(simplify your answer.)

Explanation:

Step1: Apply Geometric Mean Theorem

In a right triangle, the altitude to the hypotenuse relates the segments of the hypotenuse. The length of a leg is the geometric mean of the hypotenuse segment adjacent to it and the hypotenuse. So, \((x + 3)^2 = x \times (x + 7)\)

Step2: Expand and Simplify

Expand the left side: \(x^2 + 6x + 9 = x^2 + 7x\)
Subtract \(x^2\) from both sides: \(6x + 9 = 7x\)
Subtract \(6x\) from both sides: \(x = 9\)

Answer:

\(9\)