The perimeter of a basketball court is 114 meter and the lenght is 6 meter longer than twice the width.
What are the lenght and Width. i need help please i am stuck
just put the words into symbols
perimeter = 114
length = 2width+6
since perimeter = 2(length+width)
2(2w+6+w)=114
3w+6=57
3w=51
w=17
so, the court is 17 by 40
To find the length and width of the basketball court, you need to set up a system of equations based on the given information.
Let's assume the width of the basketball court is represented by 'w' meters.
According to the problem, the length is 6 meters longer than twice the width. This can be written as:
Length = 2w + 6
We also know that the perimeter of a rectangle is given by the equation:
Perimeter = 2(length + width)
Substituting the given perimeter (114 meters) and the expressions for length and width into the perimeter equation, we get:
114 = 2((2w + 6) + w)
Now, simplify the equation:
114 = 2(3w + 6)
Divide both sides of the equation by 2:
57 = 3w + 6
Subtract 6 from both sides:
51 = 3w
Divide both sides by 3:
w = 17
Now that we have the width (w), we can substitute it back into the expression for the length:
Length = 2w + 6
Length = 2(17) + 6
Length = 34 + 6
Length = 40
Therefore, the width of the basketball court is 17 meters, and the length is 40 meters.