Question

The perimeter of a rectangular sheet of metal is 120 feet, and the area is 800 square feet. The length and width of the rectangular sheet of metal are each multiplied by 6. What is the perimeter of the new sheet?
Select one:
a. 720 ft
b. 180 ft
c. 570 ft
d. 245 ft

Answer 1

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