Question

The length of a rectangle is 8 centimeters less than twice its width. The perimeter of the rectangle is 50 cm. What are the dimensions of the rectangle?

Answer 1

The first thing we should ask ourselves is "What is the formula for the perimeter of a rectangle?"

You may recall that this is 2L + 2W. So 2L + 2W = 50.

We also know that "The length of a rectangle is 8 centimeters less than twice its width." So we need to show this algebraically.

L = 2W - 8.

Now, we can substitute this into our original equation, so we're left with only one variable.

2L + 2W = 50.
2(2W - 8) + 2W = 50.

Now it's just a matter of simplifying our equation.

4W - 16 + 2W = 50.
6W - 16 = 50.
6W = 66.
W = 11.

Now we just need to figure out length. There are two ways to do this. We can use our original perimeter formula:

2L + 2W = 50.
2L + 22 = 50.
2L = 28.
L = 14.

Or we can use our length formula:

L = 2W - 8.
L = 22 - 8.
L = 14.

In either case, we have our answer: The dimensions of the rectangle are 14x11, or 11x14.

Answer 2

Thanks!