Question 152692: By adding the same amount to its length and its width, a developer increased the area of a rectangular lot by 3000 m^2 to make it 80 m by 100 m. What were the original dimensions of the lot?
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! (80-x)(100-x)=80*100-3,000
8,000-100x-80x+x^2=8,000-3,000
x^2-180x+8,000-8,000+3,000=0
x^2-180x+3,000=0
x^2-180x+3,000)=0
using the quadratic equation: we get:
x=(180+-sqrt[-180^2-4*1*3,000])/2*1
x=(180+-sqrt[32,400-12,000)/2
x=(180+-sqrt[20,400])/2
x=(180+-142.83/2
x=(180-142.83)/2
x=37.17/2
x=18.58 is the increase in length & width.
proof:
(80-18.58)(100-18.58)=5,000
61.42*81.42=5,000
(thus the original measurement was 61.42m & 81.42m)
5,000=5,000
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