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