Question

A 5cm piece of wire is cut into two parts such that a square formed by bending on part will have four times the area of a square formed by bending the other part, what is the length of the longer part.

Answer 1

let the piece formed into the first square be x cm
then the piece formed into the second square is 5-x cm

area of first square = (x/4)^2 = x^2/16
area of 2nd square = (5-x)^2/16

4x^2/16 = (5-x)^2/16
4x^2 = 25 - 10x + x^2
3x^2 + 10x - 25 = 0
(3x-5)(x+5) = 0
x = 5/3 or x = -5, the last part makes no sense

so one part is 5/3 cm
the other part is 5 - 5/3 or 10/3 cm

check:
area of smaller is (5/12)^2 = 25/144
area of larger is (10/12)^2 = 100/144 , which is 4 times as large.