SOLUTION: A square and a rectangle have the same area. The length of the side of the is 6CM longer than the width of the rectangle. The length of the rectangle is 5CM longer than twice the s

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Question 1056145: A square and a rectangle have the same area. The length of the side of the is 6CM longer than the width of the rectangle. The length of the rectangle is 5CM longer than twice the side of the square. Find the dimensions of the square and the rectangle. It's pretty much problem solving T.T
Answer by ankor@dixie-net.com(22740) (Show Source):
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A square and a rectangle have the same area.
The length of the side of the square is 6CM longer than the width of the rectangle.
The length of the rectangle is 5CM longer than twice the side of the square. Find the dimensions of the square and the rectangle
:
let x = the side of the square
then
x^2 = the area of the square
:
(x-6) = one side of the rectangle
and
(2x+5) = the other side of the rectangle
:
The areas are given as equal, therefore:
(2x+5)*(x-6) = x^2
FOIL
2x^2 - 12s + 5x - 30 = x^2
2x^2 - x^2 - 7x - 30 = 0
x^2 - 7x - 30 = 0
this factors to
(x+3)(x-10) = 0
the positive solution
x = 10 cm is the side of the square
and
10 - 6 = 4 cm is the width of the rectangle
and
2(10) + 5 = 25 cm is the length
:
note that the area of both = 100