SOLUTION: A field contains 48 acres. If it were 12 rods wider and 32 rods shorter, it would still contain 48 acres. Find the number of fencing needed to enclose the field?
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Question 940576: A field contains 48 acres. If it were 12 rods wider and 32 rods shorter, it would still contain 48 acres. Find the number of fencing needed to enclose the field? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A field contains 48 acres.
If it were 12 rods wider and 32 rods shorter, it would still contain 48 acres.
Find the number of fencing needed to enclose the field?
:
let L = the length of the field in rods
let w = the width of the field in rods
:
Find the number of sq/ft in 48 acres
43560 * 48 = 2090880 sq/ft
:
1 rod = 16.5 ft, one sq/rod = 16.5^2 = 272.25 sq/ft
therefore = 7680 sq/rds in 48 acres
:
two equations
L * W = 7680
L = 7680/W
and
(L-32)*(W+12) = 7680
FOIL
LW + 12L - 32W - 384 = 7680
We know LW = 7680
7680 + 12L - 32W - 384 = 7680
subtract 7680 from both sides
12L - 32W - 384= 0
simplify, divide by 4
3L - 8W - 96
Replace L with 7680/W
3 - 8W - 96 = 0
multiply both sides by w
23040 - 8w^2 - 96w = 0
A quadratic equation
-8w^2 - 96w + 23040 = 0
Using the quadratic formula, I got a positive solution of
w = 48 rods is the width
and
7680/48 = 160 rods is the length
:
See if that checks out: (48+12)*(160-32) = 7680 also
:
"Find the number of fencing needed to enclose the field?"
2(160) + 2(48) = 416 rods of fencing required. That's 16.5*416 = 6864 ft
