A piece of wire 52 cm long is divided into two parts. Each part is made a square, the total area of the two squares will be 97cm^2. What is the length of each section of wire?
+128732 Let x be one length.....then (52-x) = the other liength
And since all sides of a square are equal, the length of each of the two sides of the respective squares is x/4 and (52 - x)/4
And we have
(x / 4)^2 + ([ (52 - x) ] / 4 )^2= 97 simplify
x^/16 + [ x^2 - 104x + 2704 ] / 16 = 97 multiply both sides by 16, simplify the left side
2x^2 - 104x + 2704 = 1552 subtract 1552 from both sides
2x^2 - 104x + 1152 = 0 divide through by 2
x^2 - 52x + 576 = 0 factor
(x - 16) ( x - 36) = 0
So....one wire is 16cm long and the other is 36 cm long
