Madelyn cut a 60-inch pipe cleaner into two equal pieces, and then she used the pieces to make a square. The sum of the areas of the squares was 117 Sq^2 in. Let x= the length of one piece. Write and solve an equation to represent the situation and find the lebgths of the two original pieces.
+128460 I don't think the pieces are "equal".......the length of each piece divided by 4 will be the side length of each respective square.......so we have.....
[x/4]^2 + [(60 - x)/4]^2 = 117 simplify
[x^2] 16 + [x^2 - 120x + 3600]/ 16 = 117 multiply through by 16 and simplify
2x^2 - 120x + 3600 = 1872 subtract 1872 from both sides
2x^2 - 120x + 1728 = 0 divide through by 2
x^2 - 60x + 864 = 0 factor
(x - 24) (x - 36) = 0
So .....one piece is 24 inches long and the other is 36 inches
Proof
[24/4]^2 + [36/4]^2 =
6^2 + 9^2 =
36 + 81 =
117 sq in
