The width of a rectangle is one half it’s length.

We can take this sentence and convert it in to an equation

Call width W, and length L

The W of a rectangle is 1/2 its L. This is close to an equation but not quite. Look at the word “is.” Something “is” something is the same as saying something = something. So replace is with = and you get, The W of a rectangle = 1/2 its L. Now get rid of the extra words W=1/2L.

Ok, now the second part. The perimeter of the rectangle is 54 centimeters. The formula for perimeter is 2W+2L. So we know that 2W+2L=54 in this situation.

Now that you have the two equations there are a few ways that you can go about solving them. I am going to use substitution.

W=1/2L

2L+2W=54

I am going to take what W equals in the first equation and substitute it for the W in the second equation.

2L+2(1/2L)=54

Now, solve for L

2L+L=54

3L=54

L=18

Now that you know what L is you can solve for W.

W=1/2L

W=1/2(18)

W=9

So the length is 18 and the width is 9.

You can check your answer by plugging in 18 and 9 into the perimeter formula and seeing if you get 54

2(18)+2(9)=?

36+18=54

x + x + 2x + 2x = 54

6x = 54

Divide both by 6.

x = 9

Now if the width is x, and the length is 2x, then:

width = 9

length = 18

the lenth- 27