SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 14 (Medium)

Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathMedium

The length of a rectangle is $3$ centimeters greater than its width. The area of the rectangle is $70$ square centimeters. What is the width, in centimeters, of the rectangle?

$5$

$7$

$10$

$14$

Show answer and explanation

Answer: B

Let the width be $w$ , so the length is $w + 3$ . Then $w(w + 3) = 70$ , so $w^2 + 3w - 70 = 0$ and $(w + 10)(w - 7) = 0$ . Since a width must be positive, $w = 7$ .

Choice C is the length of the rectangle, not its width.

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