A piece of wire 52cm long is cut into two parts, each of the wire is bent to form a square. If the sum of the area of the two squares is 89. Find the perimeter of each square.

Side lengths of the squares are x and y

4x+4y=52

divide both sides by 4 for simlicity

x+y=13

area is 89 so

x²+y²=89

ok

so

x+y=13

minus x both sides

y=13-x

sub that for y in other equation

x²+y²=89

x² + (13-x) ²=89

x²+x²-26x+169=89

2x²-26x+169=89

minus 89 both sides

2x²-26x+80=0

undistribute 2

2 (x²-13x+40) = 0

factor

2 (x-8) (x-5) = 0

set to zero

x-8=0

x=8

x-5=0

x=5

x=5 or 8

find y

y=13-x

13-8=5

13-5=8

each square has side length of 5 or 8

perimiter is 4 times the area around so

5*4=20

8*4=32

the perimiters are 20cm and 32cm