the perimeter of a basketball court is 102 meters and the length is 6 meters longer than twice the width. What are the length and width?
width --- x
length --- 2x+6
2(x) + 2(2x+6) = 102
carry on
To find the length and width of the basketball court, let's solve this problem step by step:
Let's assume the width of the basketball court to be "w" meters.
According to the problem, the length is 6 meters longer than twice the width.
So, the length would be 2w + 6 meters.
The perimeter of a rectangle is given by the equation:
Perimeter = 2(length + width)
In this case, the perimeter is given as 102 meters. So we can set up the equation as follows:
102 = 2(2w + 6 + w)
Simplifying the equation:
102 = 2(3w + 6)
102 = 6w + 12
Bringing all the variables together on one side of the equation:
6w = 102 - 12
6w = 90
Now, divide both sides by 6 to solve for "w":
w = 90/6
w = 15
So, the width of the basketball court is 15 meters.
Now, substitute the value of "w" back into the equation for the length:
Length = 2w + 6
Length = 2(15) + 6
Length = 30 + 6
Length = 36
Therefore, the length of the basketball court is 36 meters and the width is 15 meters.