Question

analyze the diagram below and complete the instructions that follow. find the value of x. round the answer to the nearest tenth, if needed. a. 1.8 b. 6 c. 8 d. 20.3

Explanation:

Step1: Identify geometric relationship

In a right triangle, the altitude to the hypotenuse satisfies $\frac{\text{Adjacent segment 1}}{x} = \frac{x}{\text{Adjacent segment 2}}$

Step2: Substitute given values

Substitute segments 4 and 9:
$\frac{4}{x} = \frac{x}{9}$

Step3: Solve for $x$

Cross-multiply: $x^2 = 4 \times 9 = 36$
Take square root: $x = \sqrt{36} = 6$

Answer:

B. 6