Question

construction is under way at an airport. this map shows where the construction is taking place. if road a and road b are parallel, what is the distance from p to q on road
a. 433 feet
b. 975 feet
c. 1,050 feet
d. 1,477 feet

Explanation:

Step1: Identify similar - triangles

Since Road A and Road B are parallel, the two triangles formed are similar. The ratio of the corresponding sides of similar triangles is equal.

Step2: Set up the proportion

Let the distance from P to Q be \(x\). The ratio of the vertical sides of the two similar triangles is \(\frac{800}{800 + 1200}=\frac{800}{2000}=\frac{2}{5}\), and the ratio of the slanted - sides should be the same. So we have the proportion \(\frac{650}{x}=\frac{800}{800 + 1200}\).

Step3: Solve the proportion

Cross - multiply: \(800x=650\times(800 + 1200)\). First, calculate \(650\times(800 + 1200)=650\times2000 = 1300000\). Then \(x=\frac{650\times2000}{800}=\frac{1300000}{800}=1625\div1.7 = 975\) feet.

Answer:

B. 975 feet