The correct answer is A) 720 ft
In order to find this, we first have to find the measurements of the sides of the sheet metal. You can do this by first looking at the equations for perimeter and area, and plugging in the known values.
2l + 2w = P
2l + 2w = 120
lw = A
lw = 800
Now that we have these two, we can manipulate the perimeter formula to solve for w.
2l + 2w = 120
2w = =2l + 120
w = -l + 60.
Now that we have this, we can stick it in for w in the area equation.
lw = 800
l(-l + 60) = 800
Now we can distribute and set equal to zero to get an quadratic equation to solve.
l(-l + 60) = 800
-l^2 + 60l = 800
60l = l^2 + 800
0 = l^2 - 60l + 800
Now we can factor this into the following.
0 = (l - 40)(l - 20)
And when we look at this, it allows us to know the sides of the sheet metal as 40 and 20. Given these facts we can multiply both by 6 and then put back into the perimeter equation.
40 * 6 = 240
20 * 6 = 120
Now into the perimeter formula.
2l + 2w = P
2(240) + 2(120) = P
480 + 240 = P
720 = P
