Find the dimensions of a rectangle whose perimeter and area have the same whole number of feet and square feet?

Question

Find the dimensions of a rectangle whose perimeter and rea have the same whole number of feet and square feet? 

Length:_____         Width:_____

Answer 1

If L and W are length and width, then area=LW and perimeter=2L+2W.

Numerically, 2L+2W=LW, so 2L=LW-2W=W(L-2), W=2L/(L-2).

We can also write L=2W/(W-2).

For example, if W=3, L=6. Area=18. Perimeter=2(6+3)=18.