SOLUTION: A rectangle is 3 times as long as the width and has the same perimeter as a square whose area is 4 sq. ft larger than the rectangle. what are the dimensions of the rectangle and sq

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Question 342101: A rectangle is 3 times as long as the width and has the same perimeter as a square whose area is 4 sq. ft larger than the rectangle. what are the dimensions of the rectangle and square?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangle is 3 times as long as the width and has the same perimeter as a
square whose area is 4 sq. ft larger than the rectangle.
what are the dimensions of the rectangle and square?
:
Let x = width of the rectangle
then
3x = the length of the rectangle
then
P = 2(3x) + 2x = 8x is the perimeter of the rectangle
and
3x * x = 3x^2 = area of the rectangle
:
Let s = side of the square
then
4s = the perimeter of the square
and
s^2 = the area of the square
:
the equal perimeters equation
4s = 8x
simplify, divide by 2
s = 2x
:
That areas equation
s^2 - 3x^2 = 4
replace s with 2x
(2x)^2 - 3x^2 = 4
4x^2 - 3x^2 = 4
x^2 = 4
x = 2 ft is the width of the rectangle
then
3(2) = 6 ft is the length of the rectangle
:
Find the side of the square
s = 2(2)
s = 4 ft is the side of the square
:
:
Check solutions by finding the perimeter
Rectangle: 2(6) + 2(2) = 16 ft
Square: 4 * 4 = 16 ft
:
Check the areas
4^2 - (6*2) = 4