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HELP ME PLEASE!!! HELPPP!!! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and an area of 500 ft2. Which of the following could be the pool's length and width? 15 feet and 30 feet, 10 feet and 35 feet ,50 feet and 10 feet, 25 feet and 20 feet​

1 Answer

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Answer:

(d) 25 feet and 20 feet​

Explanation:

You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.

Area

The area is the product of the length and width. The area of the pools offered in the answer choices are ...

(a) 15·30 = 450 . . . square feet

(b) 10·35 = 350 . . . square feet

(c) 50·10 = 500 . . . square feet

(d) 25·20 = 500 . . . square feet

The area requirement eliminates answer choices A and B.

Perimeter

The perimeter is twice the sum of length and width. The perimeters of the possible pools are ...

(c) 2(50 +10) = 120 . . . feet

(d) 2(25 +20) = 90 . . . feet

The perimeter requirement eliminates answer choice C.

The pool's possible length and width are 25 feet and 20 feet, choice D.

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Additional comment

You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.

If x is the width, then 45-x is the length, and the area is ...

x(45 -x) = 500

x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square

x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension

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