SOLUTION: The side of one square is 4 in longer than that of a second square. The area of the larger is 32 sq. in less than twice the area of the smaller. Find the perimeter of each squa

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Question 631025: The side of one square is 4 in longer than that of a second square. The area of the
larger is 32 sq. in less than twice the area of the smaller. Find the perimeter of each
square.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The side of one square is 4 in longer than that of a second square.
The area of the larger is 32 sq. in less than twice the area of the smaller.
Find the perimeter of each square.
:
Let x = the side of the smaller square
then
x^2 = area of the smaller square
:
(x+4) = side of the larger square
then
(x+4)^2 = area of the larger square
:
"The area of the larger is 32 sq. in less than twice the area of the smaller."
(x+4)^2 = 2x^2 - 32
FOIL
x^2 + 8x + 16 = 2x^2 - 32
0 = 2x^2 - x^2 - 8x - 32 - 16
A quadratic equation
x^2 - 8x - 48 = 0
Factors to
(x-12)(x+4) = 0
the positive solution
x = 12 inches the side of the smaller square
4(12) = 48 in, the perimeter
and
12+4 = 16 inches the side of the larger square
4(16) = 64 inches the perimeter



square.