A rectangular garden has a side length of x+7 and a width of 3x+3. What algebraic expression would represent the perimeter of the garden?

Step-by-step explanation:

It may help you to begin by drawing a picture to model this problem, labeling one side of the rectangle x+2 and the other side 2x-3 (although this step is not necessary).

1) Perimeter: The perimeter of a shape is the distance around the outside.  Generally you just add up the side lengths.  In the case of a rectangle, since the two lengths are the same and the two widths are the same, it can be shortened to the following formula:

P=2l+2w

All that needs to be done is to substitute the expressions given for length and width into the formula above:

P=2(x+2)+2(2x-3)

Then you just need to simplify the expression on the right by distributing and combining like terms:

P=2x+4+4x-6

P=6x-2

So the expression for the perimeter of the garden is 6x-2.

2) Area: The area of a shape is the amount of space inside of it (for which the formulas vary widely depending on the shape).  The formula for the area of a rectangle is

A=l*w

Once again, you just need to substitute the given expressions for length and width:

A=(x+2)*(2x-3)

In order to simplify, you will need to distribute the binomials (often call the FOIL method) and combine like terms:

A=2x^2-3x+4x-6

A=2x^2+x-6

So this is the expression for the area of the garden.