The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and width

Answer 1

w + 2w + 6 = 57

3w = 51

w = 7

Answer 2

Amanda, you'll want to use a variable to help relate the 2 sides of the court and plug these into the perimeter of a rectangle equation (i.e., the standard shape of a basketball court).

So, as you have probably studied, the perimeter of a rectangle is given by P = 2•L + 2•W. Since we are given the perimeter, 114 m, we can use this to solve for L (length) and W (width) if we can find an expression for these entities in terms of a single variable, let's use W:

If we set W equal to rectangle's width, then L can be expressed in terms of W using the given information. That is, the 2 sides of the rectangle could be expressed as:

Width = W

Length = 2W + 6 → (6 m longer than twice the width)

Plugging these expressions into the perimeter equation gives us the following:

114 = 2(2W + 6) + 2•W

Distribute 2 across the 2W + 6 term:

114 = 4•W + 12 + 2•W

Simplify (combine like-terms):

114 = 6W + 12

102 = 6W

W = 17 meters

Now we are ready to solve for the length, L, by plugging in our value we have determined for W:

L = 2W + 6

L = 2•17 + 6

L = 40 meters

Let's check our answer:

1) Is the length 6 meters more than twice the width? → L = 2W + 6

40 = 2•17 + 6, yes, 40 = 40

2) Do the two side lengths work in our perimeter equation? → P = 2•L + 2•W

P = 2•40 + 2•17 = 114, yes, we got it right !

Hope this helps,

Todd