The perimeter of a rectangle is 70 centimeters. The length of... | SAT Systems of two linear equations in two variables Question, Answer Explained

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The perimeter of a rectangle is $70$ centimeters. The length of the rectangle is $7$ centimeters less than twice its width. What is the length, in centimeters, of the rectangle?

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Answer: 21

Let $L$ be the length and $w$ the width. Then $2L + 2w = 70$ , so $L + w = 35$ , and $L = 2w - 7$ . Substituting gives $2w - 7 + w = 35$ , so $3w = 42$ and $w = 14$ . The length is $L = 2(14) - 7 = 21$ .

Answering $14$ gives the width, not the length.

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