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?
:
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
{{{2090880/272.25}}} = 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{{{7680/w}}} - 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