Digital PSAT Math Practice Question 236: Answer and Explanation

Question: 236

In the figure above, 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 and a height of 4. You can plug this into the formula for the area of a triangle to obtain the base of the triangle, CD.

. Divide both sides by 2 to get that the base, CD = 10. Therefore, the base of triangle ABD, BD, is 8 + 10 = 18. Next, you need to find the height of triangle ABD. You 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. Plug 7.2 in for the height and 18 in for the base in the area equation: