Question

The area of a storage shed floor is 20 ft2. The length is 3 more than twice the width. Find the dimensions of the storage shed floor

Answer 1

• 2.5 ft wide
• 8 ft long

Explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

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Given relation

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

A = LW

20 = (2x+3)(x) . . . . . area of the shed

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Solution

Completing the square gives ...

2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

2(x +0.75)² = 21.125 . . . . . . . write as a square

x +0.75 = √10.5625 . . . . . divide by 2, take the square root

x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.