-The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters?
Let's denote the width of the rectangle as x and the length as 3x (since the length is equal to triple the width).
The perimeter of a rectangle can be calculated using the formula:
Perimeter = 2(length + width)
In this case, the perimeter is given as 86 centimeters. So we have:
86 = 2(3x + x)
Simplifying this equation gives us:
86 = 2(4x)
Dividing both sides by 2 gives:
43 = 4x
Finally, dividing both sides by 4 gives:
x = 10.75
So the width of the rectangle is 10.75 centimeters, and the length is 3x = 3(10.75) = 32.25 centimeters.
Thus, the system of equations to find the dimensions of the rectangle is:
x = 10.75
length = 3x = 32.25