Question

1. find x using similar right triangles (redraw triangles) x =

Explanation:

Step1: Recall geometric mean theorem

In a right triangle, the altitude to the hypotenuse is the geometric mean of the segments into which it divides the hypotenuse. So, \( x = \sqrt{36\times64} \).

Step2: Calculate the product inside the square root

First, calculate \( 36\times64 = 2304 \).

Step3: Take the square root

Then, \( \sqrt{2304} = 48 \).

Answer:

\( 48 \)