A rectangular animal pen with area 1200^2 has one side along a ... Help!?

Question

A rectangular animal pen with area of 1200^2 has one side along a barn. The other three sides are enclosed by 100 of fencing. Find the dimensions of the pen.

notthejake · Accepted Answer

let x be the distance perpendicular to the barn (using a total of 2x worth of fence)
the side parallel to the barn must be 100 - 2x

area = length * width = x(100 - 2x) = 1200
100x - 2x^2 = 1200
2x^2 - 100x + 1200 = 0
x^2 - 50x + 600 = 0
(x -30)(x - 20) = 0

so either x = 30 or x = 20

if x = 30, then the other side is 100 - 60 = 40
if x = 20, then the other side is 100 - 40 = 60

so the pen is either 30 * 40 or 20 by 60 
(the first length is the dimension perpendicular to the barn, and doubled)

30 * 40 = 1200
30(2) + 40 = 100
20 * 60 = 1200
20(2) + 60 = 100
checks...

sv · Answer

100 = 60 + 40 where (60/2)*(40) = 1200dimensions are 40 x 30

A rectangular animal pen with area 1200^2 has one side along a ... Help!?

2 Answers