Question

The width of a rectangular playground is 2x -5 feet and the length is 3x+9 feet write the polynomials that represent the area and the perimeter of the playground

Answer 1

Part 1)
`A(x)=6x^(2) +3x-45`

Part 2)
`P(x)=10x+8`

Explanation:

Let

L -----> the length of a rectangular playground

W ---> the width of a rectangular playground

we have

`W=(2x-5)\ ft`

`L=(3x+9)\ ft`

step 1

Find the area of the playground

The area of a rectangle is equal to

`A=LW`

substitute the given values

`A(x)=(3x+9)(2x-5)\\A(x)=6x^(2) -15x+18x-45\\A(x)=6x^(2) +3x-45`

step 2

Find the perimeter of the playground

The perimeter of a rectangle is equal to

`P=2(L+W)`

substitute the given values

`P(x)=2((3x+9)+(2x-5))`

`P(x)=2(5x+4)`

`P(x)=10x+8`