A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7

Question

A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?

Accepted Answer

The correct answer is 5 . Let x represent the width, in inches, of the rectangle. It's given that the length of the rectangle is 4 inches less than 7 times its width, or 7 x - 4 inches. The area of a rectangle is equal to its width multiplied by its length. Multiplying the width, x inches, by the length, 7 x - 4 inches, yields x 7 x - 4 square inches. It&rsquo;s given that the rectangle has an area of 155 square inches, so it follows that x 7 x - 4 = 155 , or 7 x 2 - 4 x = 155 . Subtracting 155 from both sides of this equation yields 7 x 2 - 4 x - 155 = 0 . Factoring the left-hand side of this equation yields 7 x + 31 x - 5 = 0 . Applying the zero product property to this equation yields two solutions: x = - 31 7 and x = 5 . Since x is the rectangle&rsquo;s width, in inches, which must be positive, the value of x is 5 . Therefore, the width of the rectangle, in inches, is 5 .

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