Question

The rectangle has a length of 4x+3 and a width of 3x. Show your work.

A. Find the perimeter.


B. Find the area.


C. Find the perimeter and area if x = 8.

Answer 1

a)
`P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6`

b)
`A= 12x^2 +9x`

c)
`P = 14*8 +6 = 112+6 = 118`

`A= 12(8)^2 +9*8 = 840`

Explanation:

We know that the length is 4x+3 and the width is of 3x

Part a

For this case the perimeter is given by:

`P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6`

Part b

The area is given by:

`A= (4x+3) (3x)`

And after multiply we got:

`A= 12x^2 +9x`

Part c

For this case replacing the value of x =8 we got:

`P = 14*8 +6 = 112+6 = 118`

`A= 12(8)^2 +9*8 = 840`

Answer 2

A. P = 14x+6

B. A = 12x^2 +9x

C. P = 118; A = 840

Explanation:

A. The perimeter is twice the sum of length and width:

P = 2(L +W) = 2((4x+3) +(3x)) = 2(7x +3)

P = 14x +6 . . . . the perimeter of the rectangle

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B. The area is the product of length and width:

A = LW = (4x +3)(3x)

A = 12x^2 +9x . . . . . the area of the rectangle

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C. When x = 8, these values are ...

P = 14·8 +6 = 118 . . . . . perimeter in units

A = 12·8^2 +9·8 = 768 +72 = 840 . . . . . area in square units