Question

1. mr. bob wants to build a bridge across the creek that runs through his property. he made the measurements and drew the map shown below. how long is the bridge? a. 18 feet b. 24 feet c. 12 feet d. 9 feet

Explanation:

Step1: Identify similar triangles

The two right - angled triangles in the figure are similar. The larger triangle has vertical side 24 ft and horizontal side 18 ft, and the smaller triangle has horizontal side 9 ft.

Step2: Set up proportion

Since the triangles are similar, the ratios of their corresponding sides are equal. Let the length of the bridge (vertical side of the smaller triangle) be $x$. We have the proportion $\frac{x}{24}=\frac{9}{18}$.

Step3: Solve the proportion

Cross - multiply: $18x = 24\times9$. Then $18x=216$. Divide both sides by 18: $x=\frac{216}{18}=12$.

Answer:

c. 12 feet