SOLUTION: A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The length of a side of the square is thirty feet. Which equ

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Question 329404: A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The length of a side of the square is thirty feet. Which equations would help you solve for the dimensions of the rectangle?
What are the dimensions of the rectangle?

I really need help on this any help is appreciated !!!
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle and a square have the same area.
The length of the rectangle is seventy feet more than two times its width.
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Let width be W.
Then length = 2W+70
And Area = W(2W+70) = 2W^2+70W
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The length of a side of the square is thirty feet.
Area of square = 30^2 = 900 sq ft.
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Which equations would help you solve for the dimensions of the rectangle?
What are the dimensions of the rectangle?
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Area of rectangle = Area of square
2W^2+70W = 900
W^2 + 35W - 450 = 0
Factor:
(W+45)(W-10) = 0
Positive solution:
W = 10 ft (width of the rectangle)
Since length = 2W+70, length = 20+70 = 90 ft
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Cheers,
Stan H.
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let width of rectangle be x
length will be 2x+70
Area of rectangle = length * width
=x(2x+70)
..
Area of square = L^2
L= 30
area = 30^2= 900
..
But the area of square = area of rectangle
x(2x+70)=900
2x^2+70x=900
divide by 2
x^2+35x=450
x^2+35x-450=0
x^2+45x-10x-450=0
x(x+45)-10(x+45)=0
(x+45)(x-10)=0
x=-45 OR x=10
ignore the negative value
width = 10
Length = 2x +70
= 2*10+70= 90 feet length
CHECK
AREA = 90*10 =900 square feet