The perimeter of a basketball court is 84 meters and the length is 6 meters longer than twice the width. What are the length and​ width?

Answer 1

Given:

Perimeter = 84 meters

Length = 2 × Width + 6

Express Length in terms of Width

L = 2W + 6

Use the Perimeter formula for a rectangle

Perimeter = 2(Length + Width)

84 = 2(L + W)

Substitute L from Step 1 into the Perimeter formula

84 = 2((2W + 6) + W)

84 = 2(3W + 6)

Solve for W

84 = 6W + 12

72 = 6W

W = 12

Find the Length

L = 2W + 6

L = 2 × 12 + 6

L = 30

The dimensions of the basketball court are:

- *Length*: 30 meters

- *Width*: 12 meters

Answer 2

For this you are going to want to put it into an equation. You can have L=length and W=width. The equation for perimeter is Perimeter = L + L + W + W because there are two ends to the court and two sides. In this problem length (L) is 6 meters longer than twice the width (W). This can be translated to:

L = 2W + 6 meters

The next step would be to substitute L in the perimeter equation with what we just did above.

Perimeter = (2W + 6) + (2W + 6) + W + W

You could simplify this by combining like terms:

Perimeter = 2(2W + 6) + 2W

We would then substitute in the information that was given in the problem, that perimeter is 84 feet.

84 = 2(2W + 6) + 2W

And now we would want to distribute the 2 outside the parentheses onto what is inside:

84 = 4W + 12 + 2W

We can now combine the terms with W attached to them.

84 = 6W + 12

Now subtract the 12 from each side.

72 = 6W

Now, to get the W by itself, you would divide the 6W by 6 and the 72 by 6.

12 = W

We just found that the width is 12 meters. Now plug this information into the formula that we found for the length (L) earlier.

L = 2W + 6

L = 2(12) + 6

L = 24 + 6

L = 30

The length is equal to 30 meters.

To check the answers you can put them back into the original perimeter equation.

Perimeter = L + L + W + W

84 = 30 + 30 + 12 + 12

84 = 60 + 24

84 = 84