PSAT Math Grid-Ins Question 135: Answer and Explanation

Question: 135

One face of a triangular building is portrayed in a photograph in which 1 inch in the photograph corresponds to 10 feet in the actual building. If the face of the actual building has an area of 960 square feet and a base of 48 feet, what is the building's height (in inches) in the photograph?

Correct Answer: 4

Explanation:

(4) The formula for the area of a triangle is . Plug the given numbers in to solve for the building's actual height:

Divide both sides by (in other words, multiply both sides by the reciprocal, 2):

1,920 = 48H

Isolate H by dividing both sides by 48:

H = 40 feet

This is the building's actual height, but we want to know its height in the picture. Let's set up a proportion to find the height in the photograph:

If we cross multiply:

(1)(40) = 10x

Dividing both sides by 10 gives:

x = 4