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Perimeter=2*L + 2*W
Area = L*W
Let L=length and W=width of your rectangle
If Perimeter=32, then
If Area=60, then
Let's take (1), and express L in terms of W:
2L + 2W = 32
L + W = 16 (divide bot sides by 2)
L = 16-W (subtract W from both sides)
We can now substitute this value of L in (2), so:
(Add W^2-16W on both sides)
If we take W-6=0,
W=6 and L=16-W=16-6=10 inches, so our rectangle is 6 inches wide and 10 inches long
If we take W-10=0
W=10 and L=16-10=6 inches, but generally length is longer than width so we just take the first solution.