Question 109613: A square and a rectangle have the same area. The length of the rectangle is 8 in. more than a side of the square, and the width of the rectangle is 4 in. less than a side of the square. Find the length of a side of the square.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A square and a rectangle have the same area. The length of the rectangle is 8 in. more than a side of the square, and the width of the rectangle is 4 in. less than a side of the square. Find the length of a side of the square.
;
Let x = side of the square
then
x^2 = area of the square
:
The rectangle:
It says,"The length of the rectangle is 8 in. more than a side of the square,:
L = (x+8)
and
It says,"the width of the rectangle is 4 in. less than a side of the square."
W = (x-4)
:
(x+8)(x-4) = area of the rectangle
(x^2 + 4x - 32) = area of the rectangles also(FOILed the demensions)
:
It said the area of the rectangle = area of the square; therefore
x^2 + 4x - 32 = x^2
:
x^2 - x^2 + 4x = 32
:
4x = 32
:
x = 8 in is the side of the square
:
:
Check our solution, find out if the square and the rectangle have the same area
(8+8)*8-4) =
16 * 4 = 64
and
8 * 8 = 64
:
Did this make sense to you, any questions?
|
|
|
