The perimeter of a rectangle is 66m. The width is 9m less than the length. What is the length and width of the rectangle?
Let's restate what facts are given in this question and what we're left to figure out. First off, we know that the perimeter of the rectangle is 66 (the perimeter, of course, is the length of all four sides of the rectangle added together).
We also know that the width of the perimeter is 9 less than the length.
w = l – 9
So how do we figure out the answer to this question? Fortunately, there's a formula we can use to plug in our values that will help us with our calculation. That formula is p = 2l + 2w, which translates to English as "the perimeter of a rectangle is equal to two times the length plus two times the width."
We know the value of the rectangle's perimeter, so we can replace p with 66 in our equation.
66 = 2l + 2w
We also know that the width of the rectangle is 9 less than the length, so we can replace the w of the equation with (l – 9).
66 = 2l + 2(l – 9)
Now, we're ready to solve the equation for length (l), since that's the remaining value in the equation that we have not yet discovered. To do this, we will multiply 2 by both values within the parentheses. 2 multiplied by lequals 2l. 2 multiplied by –9 equals –18.
66 = 2l + 2l – 18
What do we do next? We're still solving the equation for l, so we need to remove the -18 from the right side of the equation by adding it to the 66 on the left. We can also add 2l to 2l. Doing so leaves us with . . .
84 = 4l
We're almost there! Divide both parts of the equation by 4, and we'll finally know the length of the rectangle. 84 divided by 4 equals 21 (and of course 4l divided by 4 equals l), so the value of l equals 21. We know that the width of the rectangle is 9 less than the length, so we can calculate the width to equal 21 – 9, or 12m. And we even showed our work!