But what we do want to know is what w is. so go back to equation 1 that had length and width equal to the area, and solve for w:
900 = lw
900 = (15√2)w
w = 900 / (15√2)
w = 60 / √2
simplify:
w = 60√2 / 2
w = 30√2
So our length is 15√2, or about 21.21 m
Our width is 30√2, or about 42.43 m
The total amount of the fencing material that you need should then be 4l + 2w. let's solve for that f using both of our equations containing f to make sure:
f = 4l + 2w
f = 4(15√2) + 2(30√2)
f = 60√2 + 60√2
f = 120√2 m
second equation:
f = 4l + 1800/l
f = 4(15√2) + 1800/(15√2)
f = 60√2 + 120/√2
f = 60√2 + 120√2 / 2
f = 60√2 + 60√2
f = 120√2 m
We get the same f both times. So our l and w must be correct.