Let's define the variables:
Let's call the length of the rectangle "L" and the width of the rectangle "W".
Based on the given information:
The length of the rectangle is equal to triple the width: L = 3W.
The perimeter of a rectangle is found by adding up all the sides. In this case, the formula for the perimeter is:
P = 2L + 2W.
Now we can write the system of equations using the information given:
L = 3W (equation 1)
P = 2L + 2W (equation 2)
We are trying to find the dimensions of the rectangle when the perimeter is 86 centimeters. So, we substitute 86 for P in equation 2:
86 = 2L + 2W
Now, we substitute the value of L from equation 1 into equation 2:
86 = 2(3W) + 2W
Simplifying:
86 = 6W + 2W
Combining like terms:
86 = 8W
Now, we solve for W by dividing both sides of the equation by 8:
86/8 = W
10.75 = W
So, the width of the rectangle is 10.75 centimeters.
To find the length, we substitute the value of W into equation 1:
L = 3(10.75)
L = 32.25
Therefore, the length of the rectangle is 32.25 centimeters.
So, the dimensions of the rectangle are:
Length = 32.25 centimeters
Width = 10.75 centimeters.
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?
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