The perimeter of a rectangle is 14 inches and the area is 12 square inches. Find the length and width of the rectangle.
A) 6 inches and 8 inches
B) 6 inches and 4 inches
C) 3 inches and 4 inches

Question

Quizplus · Accepted Answer

Let the length of the rectangle be x and the width be y. We have two equations: 2x + 2y = 14 and xy = 12. Simplifying the first equation we get x + y = 7. Rearranging this equation we get y = 7 - x. Substituting in the second equation we get x(7 - x) = 12, which simplifies to x² - 7x + 12 = 0. Factoring this equation we get (x - 3)(x - 4) = 0, so x = 3 or x = 4. If x = 3, then y = 4 and if x = 4, then y = 3. The only option that matches these values is C. Therefore, the length is 4 inches and the width is 3 inches.

The Perimeter of a Rectangle Is 14 Inches and the Area