SOLUTION: A rectangular athletic field has a length that is 20 yards longer than its width. Its original width will be increased by 4 yds and its length will be decreased by 5 yds. The news

Question 1136533: A rectangular athletic field has a length that is 20 yards longer than its width. Its original width will be increased by 4 yds and its length will be decreased by 5 yds. The news field will have an area that is the same as the original field. Find the dimensions of the original field.
Found 2 solutions by ankor@dixie-net.com, rothauserc:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular athletic field has a length that is 20 yards longer than its width.
Its original width will be increased by 4 yds and its length will be decreased by 5 yds.
The new field will have an area that is the same as the original field.
Find the dimensions of the original field.
L = Length, W = width
:
L * W = (L-5)(W+4)
FOIL
LW = LW + 4L - 5w - 20
Subtract LW from both sides
0 = 4L - 5W - 20
"field has a length that is 20 yards longer than its width."
0 = 4(W+20) - 5W - 20
0 = 4W + 80 - 5W - 20
0 = -W + 60
W = 60 yds is the width of the original field
and
60 + 20 = 80 yds is the length
:
:
check
60 * 80 = 4800
64 * 75 = 4800

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let w be the width, and l be the length
:
l = w+20
:
(w+20) *w = Area(A)
:
1) w^2 +20w = A
:
(w+20-5) *(w+4) = A
:
(w+15) *(w+4) = A
:
2) w^2 +19w +60 = A
:
the areas are the same, so set equation 1 equal to equation 2
:
w^2 +20w = w^2 +19w +60
:
w = 60
:
l = 60 +20 = 80
:
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The dimensions of the original field are length = 80 yards and width = 60 yards
:
check the answer
:
80 * 60 = 4800 square yards
:
75 * 64 = 4800 square yards
:
answer checks
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