What are the dimensions of a rectangular garden with a perimeter of 64 meters and whose length is twice its width?

Answer 1

The formula for the perimeter of a rectangle is pretty simple: P = 2(L+W). In English, that is "The perimeter of a rectangle is two times the sum of its length and width." In your word problem, you are told that the length (which is generally considered to be the larger of the two dimensions) is twice the width. So, if the width is two meters, then the length is four; if the width is three, then the length is six, and so on. Mathematically, you write that as L = 2W. We still don't know what the actual length or width is. You now have two equations with two "unknowns," so you should have enough information to solve the problem. Using the first equation (the one for perimeter), simply replace the L with 2W. Why? Because L = 2W. P = 2(L + W) becomes P = 2(2W + W), which becomes P = 2(3W) = 6W. Since the word problem says the perimeter is 64 meters, you have 64 = 6W, so W = 64/6 = 10.67 meters. And since the length is twice the width, the length is 21.33 meters. You now need to check your answer to make sure you didn't have a brain cramp. Does two times the sum of the length and width equal 64? It better. Let's see. The sum of 10.67 and 21.33 is 32. Twice that is 64. Nice!