Question 452164
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