SAT Math Multiple Choice Question 940: Answer and Explanation

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Question: 940

8. All 50 states have legislation regarding pool safety, the majority of which includesa requirement for a safety fence around the perimeter of the top of an in-ground pool.If a rectangular in-ground pool has a length that is 2 feet less than twice its width,and the area of the top of the pool is 480 square feet, how many linear feet of fencingare required, assuming the fence is placed 1 foot from the edge of the water on allsides?

  • A. 92
  • B. 100
  • C. 108
  • D. 116

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Strategic Advice: In a question like this, translate from English into math to write an equation that represents the scenario. Drawing a diagram will also be very helpful.

Getting to the Answer: First, write expressions to represent the dimensions of the pool. If you let w represent the width, and the length is 2 feet less than twice the width, then the length is 2w - 2. To find the area of a rectangle, multiply its length times its width. Here, the area is (2w - 2) × w. Set this equal to the given area, 480, and solve for w. The equation is quadratic, so solve it by factoring or by using the quadratic formula:

The solutions for w are 16 and -15. Because the width of the pool can't be negative, the width must be 16 feet. This means the length must be 2(16) - 2 = 30 feet. Now, add the 1 extra foot around all the edges to represent the fence. Drawing a diagram like the following one may help:

The new dimensions (for the fence) are 18 by 32, so the perimeter, and therefore the number of linear feet of fencing required, is 18 + 18 + 32 + 32 = 100, which is (B).

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