Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.
-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 define the variables:
Let L be the length of the rectangle.
Let W be the width of the rectangle.
We are told that "The length of a rectangle is equal to triple the width." This can be written as the equation:
L = 3W
We are also told that "the perimeter is 86 centimeters." The formula for the perimeter of a rectangle is:
2L + 2W = Perimeter
Substituting the value of L from the first equation, we have:
2(3W) + 2W = 86
Simplifying the equation, we have:
6W + 2W = 86
8W = 86
W = 10.75
Now, we can substitute the value of W into the first equation to find L:
L = 3(10.75)
L = 32.25
Therefore, the dimensions of the rectangle are:
Length = 32.25 centimeters
Width = 10.75 centimeters
The system of equations that can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters is:
L = 3W
2L + 2W = 86