PSAT Math Multiple-Choice Question 798: Answer and Explanation

Question: 798

In the figure below, both angles ABC and ECD are 90 degrees. If the area of triangle ECD is 20 square inches, the length of EC is 4 inches, and the length of BC is 8 inches, what is the area of triangle ABD?

• A. 32.4 square inches
• B. 64.8 square inches
• C. 320 square inches
• D. 640 square inches

Correct Answer: B

Explanation:

(B) Triangle ECD has an area of 20 square inches and a height of 4 inches. We can plug
this information into the formula for the area of a triangle (A = bh) to obtain the base
of the triangle, CD:
20 = b(4) = 2b
Divide both sides by 2 to get that base CD = 10 inches. Therefore, the base of triangle ABD, which is side BD, is 8 + 10 = 18 inches. Next, we need to find the height of triangle ABD. We can utilize the fact that these are similar triangles to set up a proportion:

Cross multiply:
10AB = 72
Dividing by 10 tells you that AB = 7.2 inches. Plug in 7.2 for the height and plug in 18 for the base in the area equation:
A = (18)(7.2) = 64.8
The area of triangle ABD is 64.8 square inches, which is choice (B).