Question

A farmer wants to enlarge an existing rectangular cowpen such that the total area of the new pen is twice as large as the original pen. The current pen's dimensions are 12' x 20' . The farmer wants to add 6 feet more to the long side than to the short side. Find the dimensions of the new pen.

Answer 1

The area of the original rectangular cow pen is 12*20=240
Now the question states that the new should be twice the size 240*2=480
Let x and y be the extra length of the sides.
Than (12+x)(20+y)=480
x+6=y
Sub second equation
(12+x)(20+x+6)=480
Expand the brackets
312+x^2+12x+26x=480
x^2+38x-168=0
Solve quadratic equation
x=-42 or x=4
(-42 has no physical meaning.)
Thus x=4
4+6=10=y

12+4=16
20+10=30

Check 16*30=480!
We are done