# SAT Math Multiple Choice Question 940: Answer and Explanation

Home > SAT Test > SAT Math Multiple Choice Practice Tests

### Test Information

- Use your browser's back button to return to your test results.
- Do more SAT Math Multiple Choice Practice Tests.

**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 2*w* - 2. To find the area of a rectangle, multiply its length times its width. Here, the area is (2*w* - 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).