A farmer wants to enlarge an existing rectangular pig pen such that the total area of the new pen is twice as large as the original pen. The current pen's dimensions are 21' × 32'. The farmer wants to add 9 feet more to the long side than to the the short side. Find the dimensions of the new pen.
A)7 feet × 16 feet
B)28 feet × 48 feet
C)28 feet × 39 feet
D)28 feet × 37 feet
E)28 feet × 41 feet

Question

Quizplus · Accepted Answer

The original area is 21' × 32' = 672 square feet. Doubling this area gives 1344 square feet for the new pen. Let x be the amount added to the short side; then, x + 9 is added to the long side. The new dimensions are (21 + x) by (32 + x + 9). Setting up the equation for the area: (21 + x)(32 + x + 9) = 1344. Simplifying gives x = 7, so the new dimensions are 28' × 48'.

A Farmer Wants to Enlarge an Existing Rectangular Pig Pen