Question

The length of a rectangle is 2x + 4 and the width is x + 8. If the perimeter of the rectangle is 96, use the value of x to find the length and width of the rectangle.​

Answer 1

Hey there! I'm happy to help!

The formula for the perimeter of a rectangle is 2L+2W=P where W is the width and L is the length. This is because we have our two sides that are lengths and our two sides that are widths (different values) and we add them together to see what the distance around the whole rectangle is.

So, let's insert these values into the equation.

2(2x+4)+2(x+8)=96

We use the distributive property to remove the parentheses (which is us multiplying our equations for length and width by two).

4x+8+2x+16=96

We combine the like terms.

6x+24=96

We subtract 24 from both sides.

6x=72

Divide both sides by 6.

x=12

Now that we have our value of x, we can plug it into our length and width equations to find those values.

LENGTH:

2x+4

2(12)+4

24+4

28

WIDTH:

x+8

12+8

20

So, our length is 28 and our width is 20.

Have a wonderful rest of your day and keep on learning! :D