SOLUTION: Urgent Question! Please help as soon as possibl. Due soon! Thanks! QUESTION~ A piece of wire 52 cm long is cut into 2 parts, each of which is bent into the form of a square.

Question 759217: Urgent Question! Please help as soon as possibl. Due soon! Thanks!
QUESTION~
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.
This question I am not sure how to do it but-
I know that the two parts that the wire is cut up into can be 'x' and 'y'. Therefore, x plus y equals to 52 cm.
I know that the areas of the two squares add up to 97 sq. cm. Let one area of the square be 'a' and another area be 'b'. Therefore, it would be a plus b equals to 97 sq.cm.
Please do not write too complicated things because I cannot understand it because now I am only a Year 7. I am learning simultaneous equations so it would be good if you provide me with two equations for me to work with. That way it is easier, but if you cannot use simutaneous equations its OK! Just make is simply and a Year 7 has to be able to read and understand it.
Please help me!
Thank you for your time and help! :D
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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

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