Question 139454: I'm not sure if this is in the right section, but anyway, here is the question: Alexandra constructed a rectangular pen for her dog using a side of the barn for one side and 26 meters of fencing for the remaining three sides. If the area enclosed was 72 square meters, find the dimensions of the pen. Please, help, and many, many thanks in advance.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Alexandra constructed a rectangular pen for her dog using a side of the barn for one side and 26 meters of fencing for the remaining three sides. If the area enclosed was 72 square meters, find the dimensions of the pen.
:
Since it only has 3 sides of fencing, we can write the perimeter equation:
2L + W = 26
Therefore:
W = (26-2L); use this for substitution
:
The area
L * W = 72 sq/m
:
Substitute (26-2L) for W;
L(26-2L) = 72
:
26L - 2L^2 = 72
:
-2L^2 + 26L - 72 = 0; a quadratic equation
:
Simplify, divide equation by -2
L^2 - 13L + 36 = 0
Factor to:
(L-9)(L-4) = 0
Two solutions:
L = 9 or L = 4
:
L is usually the longer dimension, use L = 9
then
W = 26 - 2L
W = 26 - 2(9)
W = 8 m is the width
:
Check the solution find the perimeter and the area:
2(9) + 8 = 26
and
9*8 = 72
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