PSAT Math Multiple-Choice Question 579: Answer and Explanation

Question: 579

Michele wants to design a floor that will have a length and width that add up to 30 feet. She also wants the area of the floor to be 216 square feet. What will the dimensions of the floor need to be?

• A. 10 feet by 20 feet
• B. 12 feet by 18 feet
• C. 14 feet by 16 feet
• D. 17 feet by 17 feet

Correct Answer: B

Explanation:

(B) This is easiest to solve if you work your way backward from the answer choices. The only answer that multiplies to give an area of 216 is choice (B):

12 × 18 = 216

If you wanted to solve this algebraically, finding the solution would be much more complicated. This question demonstrates that you should be open to plugging in answers when you anticipate a lengthy calculation. Set up two equations, one equation for the sum of the length and width and one equation for the area:

L + W = 30

L × W = 216

Use substitution to solve:

L + W = 30

L = 30 - W

Substitute this in for L in the other equation:

L × W = 216

(30 - W) × W = 216

-W² + 30W - 216 = 0

This looks rather challenging to solve by factoring, so use the quadratic formula:

If you plug in 12 as the width, you get 18 as the length. If you plug in 18 as the width, you get 12 as the length:

L × W = 216

L × 12 = 216

L = 18

L × W = 216

L × 18 = 216

L = 12

So the dimensions are 12 feet by 18 feet, regardless of what you call the length and width.