Question

9.) The area of a rectangular shaped garden is represented by the expression x³+7x² + 7x-15 ft²? If the length of one side of the garden is represented by x+3 ft, what is the width of the garden? What is the perimeter of the garden?

Answer 1

The total area of a rectangular-shaped garden is:

`x^3+7x^2+7x-15`

We have that the area of a rectangle is

`A=L\cdot W`

We have the total area given by the expression above. We also have the length, given by:

`L=x+3`

Then

`x^3+7x^2_{}+7x-15=(x+3)\cdot W`
`W=(x^3+7x^2+7x-15)/(x+3)`

We need to solve this polynomial division:

Therefore, the width is

`x^2+4x-5`

The perimeter is the sum of all the sides of the rectangle:

`2W+2L\rightarrow2\cdot(x^2+4x-5)+2\cdot(x+3)=(2x^2+8x-10)+2x+6`
`2x^2+10x-4`

So, the perimeter is 2x^2+10x-4.

The width is x^2+4x-5.