Please help. Find the dimensions of a rectangle that has a perimeter of 16cm and area of 13 cm^2

2x+2y=16
xy=13

xy=13
x=13/y

2x+2y=16
2(13/y)+2y=16
(26/y)+(2y^2/y)=16y/y
26+2y^2=16y
2y^2-16y+26=0
2(y^2-8y+13)=0
y^2-8y+13=0
y=5.7 or y=2.3

xy=13
x(5.7)=13
x=13/(5.7)
x=2.3 when y=5.7

OR

xy=13
x(2.3)=13
x=13/(2.3)
x=5.7 when y=2.3

In this case, you happen to get the same answers for both possibilities.

Answer: 5.7cm and 2.3 cm