SOLUTION: a rectangle has its length of 2 ft greater than its width.if the lenghth is increased by 3 ft and the width by 1 ft, the area of the new rectangle will be twice the area of the old

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Question 755384: a rectangle has its length of 2 ft greater than its width.if the lenghth is increased by 3 ft and the width by 1 ft, the area of the new rectangle will be twice the area of the old one. what is the lenghth and width of the original rectangle
Answer by lwsshak3(11628) About Me  (Show Source):
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a rectangle has its length of 2 ft greater than its width.if the length is increased by 3 ft and the width by 1 ft, the area of the new rectangle will be twice the area of the old one. what is the length and width of the original rectangle
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let x=width of original rectangle
x+2=length of original rectangle
area of original rectangle=x(x+2)=x^2+2x
..
x+1=width of new rectangle
x+2+3=length of new rectangle
area of new rectangle=(x+1)(x+5)=x^2+6x+5
...
x^2+6x+5=2(x^2+2x)
x^2+6x+5=2x^2+4x
x^2-2x-5=0
..
solve for x using following quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-2, c=-5
x=-1.55 (reject)
x=3.45
x+2=5.45
width of original rectangle=3.45 ft
length of original rectangle=5.45 ft