Question

The dimensions of a rectangular building are given as a length of 12x + 24 feet and a width of 20x - 10 feet.

Write the expression that represents the area of the building, in terms of x.
Write the expression that represents the perimeter of the building, in terms of x.
If the perimeter is going to be 220 feet, what are the dimensions of the building.

Answer 1

120(2x² + 3x - 2) or 240x² + 360x - 240

Perimeter = 64x + 28

x = 3

Length = 60ft

Width = 50ft

Explanation:

Area = (12x + 24)(20x - 10)

= 12(x + 2).10(2x - 1)

= 120(2x² + 3x - 2)

= 240x² + 360x - 240

Perimeter = 2(12x + 24) + 2(20x - 10)

= 24x + 48 + 40x - 20

= 64x + 28

64x + 28 = 220

64x = 192

x = 3

Length = 12(3) + 24

= 36 + 24

= 60

Width = 20(3) - 10

= 60 - 10

= 50

Answer 2

• area: (12x +24)(20x -10)
• perimeter: 64x +28
• 60 ft long by 50 ft wide

Explanation:

The area of the building is given by the formula ...

A = LW

A = (12x +24)(20x -10) . . . . . substitute given length and width

__

The perimeter is twice the sum of length and width:

P = 2(L +W)

P = 2((12x +24) +(20x -10)) = 2(32x +14)

P = 64x +28

__

If the perimeter is 220 feet, we can use that fact to find the value of x.

220 = 64x +28

192 = 64x . . . . . . . subtract 28

3 = x . . . . . . . . . . . divide by 64

Then the dimensions of the building are ...

length = 12x +24 = 12(3) +24 = 60 . . . feet

width = 20x -10 = 20(3) -10 = 50 . . . feet

The length and width of the building are 60 feet and 50 feet, respectively.