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?

Answer 1

800 = l(w)
120 = 2l + 2w
800 = 20(40)
120 = 2(40) + 2(20)
40(6)=240
20(6)=120
P=2(240) + 2(120)
P=480+240
P=720
Answer: Perimeter is 720ft

Answer 2

The perimeter of the new sheet is 720 feet.

Let the old length = x and the width= y.

So, periemeter = 2(x + y) = 120 or, x + y = 60 or,  y = 60 - x .......(1)

Area = xy = 800.

Plug y = 60 - x and solve for x.

$x(60-x)=800\\60x-x^2=800\\x^2-60x+800=0\\(x-20)(x-40)=0\\x=20, 40$

For x = 20, y = 60 - 20 = 40.

For x = 40, y = 60 - 40 = 20.

So dimensions are 20 ft and 40 ft.

If The length and width of the rectangular sheet of metal are each multiplied by 6.

So the new dimensions are (20*6) = 120 ft and (40*6) = 240 ft.

So the perimeter is = 2(120 + 240) = 720 ft.

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