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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Let x represent the width of the rectangle.
Since the length of the rectangle is equal to triple the width, the length can be represented as 3x.
The perimeter of a rectangle is 2 times the length plus 2 times the width. Therefore, the equation for the perimeter of the rectangle can be written as follows:
2(3x) + 2x = 86
Simplifying the equation:
6x + 2x = 86
8x = 86
Dividing both sides by 8:
x = 10.75
The width of the rectangle is 10.75 centimeters.
To find the length, substitute the width value back into the equation for the length:
Length = 3x = 3(10.75) = 32.25 centimeters
Therefore, the dimensions of the rectangle are a width of 10.75 centimeters and a length of 32.25 centimeters.