Question

A piece of wire 44cm long is cut into two parts. Each part is bent to form a square. Given that the total area of the two squares is 65cm^2, find the perimeter of each square.​

Answer 1

let x=side of one square in cm

perimeter of one square=4x

let y=side of other square in cm

perimeter of other square=4y

x^2+y^2=65

4x+4y=44

x+y=11

y=11-x

x^2+(11-x)^2=65

x^2+121-22x+x^2=65

2x^2-22x+56=0

x^2-11x+28=0

(x-4)(x-7)=0

x=4 or x=7

y=11-4=7 or y=11-7=4

So,

Perimeter of one square= 4×4=16 cm

Perimeter of other square = 4×7=28 cm

If the perimeter of one square is 16 cm, perimeter of the other square would be 28 cm or vice-versa.