SOLUTION: The area of a rectangular lot 80m by 100m is to be increased by 4000m^2. The length and the width will be increased by the same amount. What are the dimensions of the larger lot?

Question 520392: The area of a rectangular lot 80m by 100m is to be increased by 4000m^2. The length and the width will be increased by the same amount. What are the dimensions of the larger lot?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Area = Length * Width
.
A = 80 m * 100 m
A = 8000 m^2
.
The area is increased by 4000...
A = 8000 + 4000 m^2
A = 12000
.
L and W will be increased by the same amount.
What are the new dimensions?
.
x = the amount of increase
80+x = new dimension
100+x = new dimension
.
(80+x)(100+x) = 12000
.
use FOIL
.
8000 +80x +100x + x^2 = 12000
.
rearrange
.
x^2 + 180x + 8000 -12000 = 0
.
x^2 +180x -4000 = 0
.
factor
.
(x+200)(x-20) = 0
.
check using FOIL
.
x^2 -20x +200x -4000 = 0
OK
.
x = -200 or 20
.
Negative length and width are nonsense, so x = 20 is the only reasonable solution.
.
Re-read the question to be sure you answer it.
.
Answer: The dimensions of the new lot are 100 by 120 m.
.
Always check your answer.
.
100*120 = 12000 = 8000 + 4000
.
Done.
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