SOLUTION: The original dimensions of a rectangle were 15cm by 20cm. When both dimensions were decreased by the same amount, the area of the new rectangle is half the area of the original rec

Question 198910: The original dimensions of a rectangle were 15cm by 20cm. When both dimensions were decreased by the same amount, the area of the new rectangle is half the area of the original rectangle. Find the dimensions of the new rectangle. Use let statements
Answer by anantha(86) (Show Source): You can put this solution on YOUR website!
sol:
the original dimensions are 15cm and 20cm
let the dimensions are decreased by x amount
after decreasing the dimensions are 15-x,20-x
area of the original rectangle=15*20=300cm^2
now the area of the new recatngle=(15-x)*(20-x)
according to the problem
area of the new rectangle=half the area of the original rectangle
area of the new rectangle=1/2*area of the original rectangle
(15-x)(20-x)=1/2*300
(15-x)(20-x)=300/2
(15-x)(20-x)=150
15*(20-x)-x*(20-x)=150
[15*20-15*x]-[x*20-x*x]=150
[300-15x]-[20x-x^2]=150
300-15x-20x+x^2=150
300-35x+x^2=150
x^2-35x+300=150
x^2-35x+300-150=0
x^2-35x+150=0
x^2-5x-30x+150=0
x(x-5)-30(x-5)=0
(x-5)(x-30)=0
x-5=0
x=5
x-30=0
x=30
now we take x=5
the dimensions of the new rectangle=15-x,20-x
=15-5,20-5
=10,15
now we take x=30
the dimensions of the new rectangle=15-x,20-x
=15-30,20-30
=-15,-10
in this problems we always take positive values
so the dimensions of the new rectangle were 10cm,15cm
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