Question

analyze the diagram below and complete the instructions that follow.
find the value of y. round the answer to the nearest tenth, if needed.
a. 8
b. 14.7
c. 21.3
d. 27

Explanation:

Step1: Identify similar triangles

The two smaller right triangles and the large triangle are all similar, so corresponding sides are proportional.

Step2: Set up proportion

The segment of length 12 corresponds to 18, and 18 corresponds to $y$, so $\frac{12}{18}=\frac{18}{y}$

Step3: Solve for y

Cross-multiply: $12y = 18\times18$
Calculate $18\times18=324$, so $y=\frac{324}{12}=27$

Answer:

D. 27