SOLUTION: The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?

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Question 880432: The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L, width and length.
L=10%2Bw, for the first part of the description.

Each side is increased by 10 feet.
w%2B10 the increased width;
L%2B10=10%2B%28w%2B10%29=w%2B20, the increased length.

The increased dimensions makes area become 2wL, the area of the original rectangle multiplied by 2.

Find original w and L.
Original area, wL=w%28w%2B10%29=w%5E2%2B10w.
Increased area, %28w%2B10%29%28L%2B10%29=%28w%2B10%29%28w%2B20%29=w%5E2%2B30w%2B20.

We were given that increased area equals two times the original area:
highlight_green%28w%5E2%2B30w%2B20=2%28w%5E2%2B10w%29%29
w%5E2%2B30w%2B20=2w%5E2%2B40w
20=w%5E2%2B10w
w%5E2%2B10w-20=0
D=100-4*(-20)=100+80=180, sqrt(180)=sqrt(3*6*2*5)=sqrt(3*3*2*2*5)=6sqrt(5).
w=%28-10%2B6sqrt%285%29%29%2F2
Original width, highlight%28w=-5%2B3sqrt%285%29%29.
L=w%2B10
L=3sqrt%285%29-5%2B10
Original length, highlight%28L=3sqrt%285%29%2B5%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?


Width of original rectangle:   highlight_green%2820%29 feet

Length of original rectangle:  highlight_green%2830%29 feet

Area of original rectangle:    highlight_green%28600_feet%5E2%29

You can do the check!! 



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