Question 296536
2x+2y=34

2x=34-2y  Divide equation by 2

x=17-y

x^2+y^2=13^2

(17-y)^2 +y^2=13^2


289 -34y+y^2+y^2= 169

2y^2-34y+120 =0

divide equation by 2

y^2-17y+60 = 0

y^2-12y-5y+60=0

y(y-12)-5(y-12)=0

(y-12)(y-5)=0

y=12 Or 5

The sides of the rectangle are 5 and 12