SOLUTION: a farmer has 120 yards of fencing to build around a rectengular orchard. let w be the width of the orchard. write an equation giving the area of the orchard. find the dimensions of

Algebra ->  Equations -> SOLUTION: a farmer has 120 yards of fencing to build around a rectengular orchard. let w be the width of the orchard. write an equation giving the area of the orchard. find the dimensions of      Log On


   

Question 311990: a farmer has 120 yards of fencing to build around a rectengular orchard. let w be the width of the orchard. write an equation giving the area of the orchard. find the dimensions of the orchard when the area is 900 square yards
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let l be the legnth of the rectangle, w be the width of the rectangle.
The perimeter of a rectangle is
P=2%2A%28l%2Bw%29=120
1.l%2Bw=60
The area of a rectanlge is
A=l%2Aw
2.l%2Aw=900
From eq. 2,
l=900%2Fw
Substitute into eq. 1,
l%2Bw=60
900%2Fw%2Bw=60
900%2Bw%5E2=60w
w%5E2-60w%2B900=0
%28w-30%29%5E2=0
w-30=0
w=30
Then from eq. 2,
l=30
The orchard is a 30 yd x 30 yd square.