The perimeter of a rectangle is 22 inches and the area is 30 square inches. Find the length and width of the rectangle.
A)5 and 12
B)10 and 12
C)5 and 6
D)10 and 6
E)none of these

Question

Quizplus · Accepted Answer

Let the length be L and the width be W. We know that 2L + 2W = 22 or L + W = 11, and LW = 30. We can solve for L and W using substitution or elimination. By substitution, we can solve for W in the second equation to get W = 30/L. We can then substitute this expression for W into the first equation to get L + 30/L = 11. Multiplying both sides by L gives us L^2 + 30 = 11L, or L^2 - 11L + 30 = 0. This equation factors as (L - 5)(L - 6) = 0, so L = 5 or L = 6. If L = 5, then W = 30/5 = 6, and if L = 6, then W = 30/6 = 5. Therefore, the length and width of the rectangle are 5 and 6, respectively, so the best choice is C.

The Perimeter of a Rectangle Is 22 Inches and the Area