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 c?
a. 433 feet
b. 975 feet
c. 1,050 feet
d. 1,477 feet

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

Since Road A and Road B are parallel, we can use the proportion \(\frac{650}{x}=\frac{800}{1200 + 800}\). Let the distance from \(P\) to \(Q\) be \(x\).

Step2: Cross - multiply and solve for \(x\)

Cross - multiplying gives \(800x=650\times(1200 + 800)\). First, calculate \(1200+800 = 2000\). Then \(800x=650\times2000\), so \(x=\frac{650\times2000}{800}\).

$$x=\frac{650\times2000}{800}=\frac{650\times20}{8}=\frac{13000}{8}=975$$

Answer:

B. 975 feet