Start by writing out the formulas for perimeter and area:
P=2L+2W A=L*W
We know that A = L*W = 336 sq meters and that P=2L + 2W = 100m.
Let's solve the first equation for L: L = 336/W
Subst. this into the formula for perimeter: 2[336/W] + 2W = 100 m (given)
Now all you have to do is to solve this for W:
336/W + W = 50 becomes 336 + W^2 = 50W.
Then W^2 - 50W + 336 = 0. Using the quadratic formula, I found that
50 plus or minus sqrt (1156) 50 plus or minus 34
W = ---------------------------------------- = -------------------------------
2 2
W has to be positive. Thus, choose W = (50+34) / 2 = 42
Then L = 336 / W, or 336 / 42, or 8.
The dimensions of this rectangle are 8 by 42.
You should check these results. Does P = 2(8) + 2(42) = 100 ?