Question

The area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length.

• A. 30
• B. 25
• C. 35
• D. 20

Answer 1

The correct option is C

35

Let X be the length and let Y be the width.

The length is 3 more than twice the width, so X = 2Y + 3.

The area is 560, so XY= 560. Put in X = 2Y + 3 and solve for Y: XY = 560

(2Y + 3) x Y = 560

2Y${}^2$ + 3Y = 560

2Y${}^2$ + 3Y - 560 = 0

Use the Quadratic Formula: $Y=\frac{-3\pm \sqrt{9-4\left(2\right)(-560)}}{2.2}$$=\frac{-3\pm \sqrt{4489}}{4}$ $=\frac{-3\pm 67}{4}$ $=\frac{-70}{4}$ or $\frac{64}{4}$

Since the width can't be negative, we get Y = $\frac{64}{4}$ = 16.

The length is X = 2$\times$16 + 3 = 35.