PSAT Math Multiple-Choice Question 78: Answer and Explanation

Question: 78

The owner of a barn needs to paint the front of the barn's roof. As shown in the figure above, the roof measures 8 m along the bottom, and the sides of the roof meet the bottom at a 30° angle. If one bucket of paint can cover 5 m², what is the minimum number of buckets the owner needs to purchase?

• A. 1
• B. 2
• C. 3
• D. 4

Correct Answer: B

Explanation:

B

The question asks for the minimum number of buckets of paint needed to cover the front of a barn's roof. To find the answer, solve for the total area. The formula for the area of a triangle is . The figure provides that the base, b, is 8 m. The two smaller right triangles both have angles of 30° and 90°, so the other angle must be 60° in both. Since they share a side (the height), the two triangles are the same size, and the 8 m base is equally split to be 4 m for each right triangle. To find the height, use the 30°-60°-90° right triangle rule: if the short side (opposite 30°) is h, the middle side (opposite 60°) is h. Make 4 = h and divide both sides by to get h ≈ 2.4. Then set = (4)(2.4) = 9.6. To cover 9.6 m², the owner will need buckets, which is 1.92. Since 1 bucket is not enough, round up to 2. The correct answer is (B).