Question 759217
A piece of wire 52 cm long is cut into 2 parts, each of which is bent
 into the form of a square. the total area enclose by the two squares
 is 97 sq. cm. Find the sides of the two squares.
:
 Let x = the side of one square
then
 x^2 = the area of that square
and
 4x = the perimeter of that square
:
Let y = the of the other square
then
y^2 = the area of it
and
4y = the perimeter
:
Two equations
:
The length of the wire
4x + 4y = 52
simplify, divide by 4
x + y = 13
or subtract y from both sides
y = (13-x); we can use this for substitution
:
and the area of the two squares
x^2 + y^2 = 97
replace y with (13-x)
x^2 + (13-x)^2 = 97
FOIL (13-x)(13-x)
x^2 + 169 - 13x - 13x + x^2 = 97
Combine like terms
x^2 + x^2 - 26x + 169 - 97 = 0
A quadratic equation
2x^2 - 26x + 72 = 0
Simplify, divide by 2
x^2 - 13x + 36 = 0
Factors to
(x-4)(x-9) = 0
two solutions
x = 4 is the side of the first square
and
x = 9 is the side of the 2nd square
:
:\
Check this:
4(4) + 4(9) = 52
and
4^2 + 9^2 = 97