SOLUTION: A veterinarian wishes to use 156 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown in the following

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Question 1207295: A veterinarian wishes to use 156 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown in the following figure. If the total enclosed area is 864 square feet, find the width w and length l of the enclosed region.
w = ft (smaller width) by l = ft
w = ft (larger width) by l = ft
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Set up an equation for the perimeter using the total length of the fencing and the variables representing the width and length of the region.
P=2%28l%2Bw%29
if a veterinarian wishes to use 156 feet of chain-link fencing , P=156ft

156=2%28l%2Bw%29
l%2Bw=156%2F2
l%2Bw=78...solve for l
l=78-w......eq.1

if the total enclosed area is 864ft%5E2, we have

l%2Aw=864....substitute l
%2878-w%29w=864
78w-w%5E2=864
0=w%5E2-78w%2B864
using quadratic formula we get
w+=+3+%2813+%2B+sqrt%2873%29%29=64.63=>larger width
w+=+3%2813+-+sqrt%2873%29%29=13.37 =>smaller width
calculate the lengths
l=78-64.63=13.37
l=78-13.37=64.63

answer:
w=13.37ft (smaller width) by l=64.63ft
w=64.63ft (lager width) by l=13.37ft


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The lengths of fencing are the width 3 times and the length 2 times; the total is 156 feet: 3w%2B2l=156

The area of 864 square feet is length times width: lw=864

Solve the first equation for the width w and substitute in the second equation.

3w=156-2l
w=%28156-2l%29%2F3
l%28%28156-2l%29%2F3%29=864
156l-2l%5E2=2592
2l%5E2-156l%2B2592=0
l%5E2-78l%2B1296=0
%28l-24%29%28l-54%29=0

l=24 or l=54

If l=24 then w=%28156-48%29%2F3=36

First solution: length 24, width 36
CHECK: 24*36=864; 3(36)+2(24)=108+48=156

If l=54 then w=%28156-108%29%2F3=16

Second solution: length 54, width 16
CHECK: 54*16=864; 3(16)+2(54)=48+108=156

ANSWERS:
(1) width 36, length 24
(2) width 16, length 54