The perimeter of a basketball court is 108 meters and the length is 6 meters longer than twice the width. what are the length and the width?
P = 2L + 2W
108 = 2(2W + 6) + 2W
108 = 4W + 12 + 2W
108 - 12 = 6W
96 = 6W
16 = W
To find the length and width of the basketball court, we can set up a system of equations based on the given information.
Let's say the width of the court is "w" meters. According to the problem, the length is 6 meters longer than twice the width. So, the length can be represented as "2w + 6" meters.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the perimeter is given as 108 meters. Therefore, we can write the equation:
2w + 2(2w + 6) = 108
Now, let's solve this equation step by step:
2w + 2(2w + 6) = 108
2w + 4w + 12 = 108
6w + 12 = 108
6w = 108 - 12
6w = 96
w = 96/6
w = 16
So, the width of the basketball court is 16 meters.
To find the length, we substitute the value of the width into the equation for the length:
Length = 2w + 6 = 2(16) + 6 = 32 + 6 = 38
Therefore, the length of the basketball court is 38 meters, and the width is 16 meters.