Question

analyze the diagram below and complete the instructions that follow.
find the value of x.
a. 2
b. 3
c. 4
d. 5

Explanation:

Step1: Identify similar triangles

We have a right triangle with an altitude to the hypotenuse, creating two smaller similar triangles (and all three triangles are similar to each other). The side of length 6 is the geometric mean of the segment \(x\) and the full hypotenuse 9.

Step2: Set up proportion

For similar triangles, the proportion is:
$$\frac{x}{6} = \frac{6}{9}$$

Step3: Solve for \(x\)

Cross-multiply and isolate \(x\):
$$9x = 6 \times 6$$
$$9x = 36$$
$$x = \frac{36}{9} = 4$$

Answer:

C. 4