From perimeter and area to dimension

Perimeter of a rectangle: $P=2(l+w)$

Substituting in $P=32$ , we find that $l+w=16$

Area of a rectangle: $A=lw$

We know that $A=60$ and that $w=16-l$

Substituting these values into the equation for area yields the quadratic $-l^2+16l-60=0$

Factoring the quadratic will result in $l=6$ and $l=10$ .

Since we are finding the larger dimension, we conclude that $l=10$ .