SOLUTION: a wire of length 100 cm is cut into two piece and each part is bent to form a square. if the sum of the areas of the two square is 425 cm^2 find the lenghts of the sides of the two

Question 404199: a wire of length 100 cm is cut into two piece and each part is bent to form a square. if the sum of the areas of the two square is 425 cm^2 find the lenghts of the sides of the two squares
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a wire of length 100 cm is cut into two piece and each part is bent to form a square.
if the sum of the areas of the two square is 425 cm^2 find the lengths of the sides of the two squares
:
Let x = side of one square
Let y = side of the other square
then
4x + 4y = 100
simplify, divide by 4
x + y = 25
y = (25-x), use this for substitution
and
x^2 + y^2 = 425
Substitute (25-x) for y
x^2 + (25-x)^2 = 425
FOIL (25-x)(25-x)
x^2 + 625 - 50x + x^2 = 425
Arrange as a quadratic equation
x^2 + x^2 - 50x + 625 - 425 = 0
2x^2 - 50x + 200 = 0
(x-20)(2x-10) = 0
Two solutions
x = 20 is the side of one square
or
2x = 10
x = 5 is the side of one square
:
Find y
25 - 20 = 5 is the side of the other square
or
25 - 5 = 20 is the side of the other square
:
anyway, one square side is 20, the other square side is 5
:
:
See if this is true
4(20) + 4(5) =
80 + 20 = 100
and
20^2 + 5^2 = 425

RELATED QUESTIONS
A piece of wire of length 1meter is cut into two parts and each part is bent to form a... (answered by josgarithmetic,MathTherapy)

A PIECE OF WIRE 44 CM LONG IS CUT INTO TWO PARTS AND EACH PART IS BENT TO FORM A SQUARE.... (answered by Theo)

A wire 80 cm in length is cut into two parts and each part is bent to form a square. If... (answered by math_helper)

A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece if... (answered by fcabanski)

A piece of wire (56 cm long) is cut into two pieces and each piece is bent into the shape (answered by Edwin McCravy)

A wire that is 32 cm long is cut into two pieces, and each piece is bent to form a... (answered by richwmiller)

A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is (answered by josgarithmetic,ikleyn)

a wire of length 200 cm is cut into two parts and each part of wire is bent to form a... (answered by mananth)

A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece is... (answered by josmiceli)