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Question 1093108: A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 1 square feet larger than that of the rectangle. What are the dimensions of both the rectangle and the square?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let L = the length of the rectangle
let w = the width
let s = the side of the square
:
A rectangle is three times as long as it is wide
L = 3w
and has the same perimeter as a square
2L + 2W = 4s
simplify, divide by 2
L + w = 2s
replace L with 3w
3w + w = 2s
4w = 2s
simplify, divide by 2
2w = s
whose area is 1 square feet larger than that of the rectangle.
L*w + 1 = s^2
Replace L with 3w, replace s with 2w
3w^2 + 1 = (2w)^2
3w^2 + 1 = 4w^2
1 = 4w^2 - 3w^2
1 = w^2
w = 1 is the width of the rectangle
then
L = 3 is the Length of the rectangle
and the area of the rectangle
3 * 1 = 3 sq/ft
The square
s = 2(1)
s = 2 ft is the side
It's area: 2^2 = 4 sq/ft
:
What are the dimensions of both the rectangle and the square?
3 by 1, and 2 by 2
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