SOLUTION: A farmer uses 60metres of fencing to make three sides of a rectangular sheep pen, the fourth side being a wall. Find the length of the shorter sides of the pen if the area enclsed

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A farmer uses 60metres of fencing to make three sides of a rectangular sheep pen, the fourth side being a wall. Find the length of the shorter sides of the pen if the area enclsed       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 914378: A farmer uses 60metres of fencing to make three sides of a rectangular sheep pen, the fourth side being a wall. Find the length of the shorter sides of the pen if the area enclsed is 448 metre square
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
("shorter sides", length to find, so these would not be along the wall).

Dimensions x and y.
Fencing quantity is 60 meters, and area to enclose is 448 sq. m's.

Assuming y is along the wall, and another length y is opposite the wall,
x would be one of the shorter sides.

2x+y=60 to account for the length of fencing
and
xy=448 for the area.

highlight_green%28system%282x%2By=60%2Cxy=448%29%29

Substitute for y in the area equation:
x%2860-2x%29=448
simplify and solve first for x.
x%2830-x%29=224
-x%5E2%2B30x-224=0
highlight_green%28x%5E2-30x%2B224=0%29

Trying to factor that may be a chore, but the discriminant is 30%5E2-4%2A224=4, a perfect square.
x=%2830%2B-sqrt%284%29%29%2F2
x=%2832%2F2%29 or x=28%2F2
x=16 or x=14

Earlier found y=60-2x.
-------------------------
If x=16 then y=28.
If x=14 then y=32.
-------------------------