Question

The dimensions of a rectangular building used to store tools for electrical lineman has a length of 12x+24 feet and the width of 20x-10 feet.

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

Answer 1

a) Area = 2x² + 3x - 2

b) Perimeter = 64x + 28

c) Length = 60 feet and Width = 50 feet

Explanation:

It is given that:

Length of building = 12x + 24

Width of building = 20x - 10

Area = Length * Width

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

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

Area =
`240x^2-120x+480x-240`

Area =
`240x^2+360x-240 = 2x^2+3x-2`

Perimeter = 2 (Length + Width )

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

Perimeter = 64x + 28

Putting Perimeter = 220

220 = 64x + 28

64x = 220 - 28

64x = 192

Dividing both sides by 64

x = 3

Length = 12(3) + 24 = 36 + 24 = 60 feet

Width = 20(3) - 10 = 60 - 10 = 50 feet

Therefore,

a) Area = 2x² + 3x - 2

b) Perimeter = 64x + 28

c) Length = 60 feet and Width = 50 feet