A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft ². Use a quadratic equation to find the dimensions of the rectangle. A) 3 ft, 6 ft B) 5.5 ft, 9.5 ft C) 6 ft, 9 ft D) 8 ft, 11 ft E) 5 ft, 10 ft

Question

Quizplus · Accepted Answer

Let x be the width of the rectangle. Then the length is x+3. The area of the rectangle is x(x+3) = 54. This gives us a quadratic equation x^2+3x-54=0. Factoring, we get (x+9)(x-6)=0. Since the width must be positive, the only solution is x=6 ft. Then, the length is x+3=9 ft. Therefore, the dimensions are 6 ft by 9 ft, which corresponds to choice C.

A Rectangle Is 3 Ft Longer Than It Is Wide