Alex D. answered • 04/17/19
While it may not look like there is enough information here to answer the question, we can actually create multiple equations here to translate what is happening in the problem. That is called a system of equations.
We should also remember that the "border" in the problem is another way of describing the perimeter of the rectangle. The formula for the perimeter of a rectangle is "two times the width plus two times the length," or written as a formula: 2W + 2L = perimeter
We also know that in our situation, the perimeter is equal to 200. So, we can set up our first equation: 2W + 2L = 200. We can then divide both sides of the equation by 2 to get a simpler form: W + L = 100.
But we can't solve an equation that has two variables in it unless we have another, different equation we can use to help us. Luckily, the problem has more information in it. We know that the length is 4 times the width. To write that as a mathematical equation, we could say: L = 4W
At this point, we have two equations, each of which has our two variables W and L:
W + L = 100
L = 4W
Whenever you have a system of equations, you have a few different options to solve the system, but the most efficient solution here would be substitution. See how there's a single L all by itself in both equations? Since we know that L is equal to 4W, then we can substitute 4W where the L is in the first equation. That will give us a new equation:
W + 4W = 100
Now, we can combine W + 4W to be 5W. If 5W is equal to 100, then from there we can figure out the width of the rectangle (100 divided by 5 is 20). If the width is 20, and the length is 4 times the width, then the length must be 4 times 20, or 80.
Finally, we'll look back at the problem to see which units we are using. Since the problem is given to us in inches, then our final answers for the dimensions must be a width of 20 inches and a length of 80 inches.
