SOLUTION: this rectangle has length 5 units more than the side of the square and width half the sid the side of the square. if the two areas are equal, what are the rectangles dimensions
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Question 452164: this rectangle has length 5 units more than the side of the square and width half the sid the side of the square. if the two areas are equal, what are the rectangles dimensions
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
his rectangle has length 5 units more than the side of the square and width half the sidethe side of the square.
if the two areas are equal, what are the rectangles dimensions
:
Let x = side of the square
then
x^2 = area of the square
:
(x+5) = the length of the rectangle
.5x = the width of the rectangle
then
.5x(x+5) = .5x^2 + 2.5x = the area of the rectangle
:
The areas are equal, therefore:
x^2 = .5x^2 + 2.5x
x^2 - .5x^2 = 2.5x
.5x^2 = 2.5x
divide both sides by x
.5x = 2.5
Multiply both sides by 2
x = 5 is the side of the square
then
5 + 5 = 10; the length of the rectangle
and
.5(5) = 2.5; the width of the rectangle
:
:
Check this by find the areas
5^2 = 25 area of square
10*2.5 = 25 area of the rectangle
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