Question 268929
If I know the perimeter of a rectangle is 34 and the area is 60 how do I find the sides?
perimeter is 2 * (length + width) or 2L + 2W
area is length * width or L*W

2L + 2W = 34 (divide both sides by 2)
L + W = 17 (you can solve this for L to have L in terms of W, or solve for W to have W in terms of L)

L * W = 60 (so now we know the sum is 17 and the product is 60)

should subsitute in to the product equation (L*W=60) either L in terms of W and solve for W then solve for L or W in terms of L and solve for L then solve for W

L * W = 60
L * (17 - L) = 60 (substituted in)
17L - L^2 = 60 (rearrange)
-L^2 + 17L - 60 = 0 (divide both sides by -1)
L^2 - 17L + 60 = 0 (solve for L)
(L-12)(L-5) = 0 (foil: L^2 - 5L - 12L + 60)
L=5 or L=12
since L+W=17 then W=12 or W=5 

L*W = 12 * 5 = 60
2 * (L+W) = 2 * 17 = 34