3. Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.

Question

-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?

Answer 1

Let's define the variables:
Let L be the length of the rectangle.
Let W be the width of the rectangle.

From the given information, we know that the length of the rectangle is equal to triple the width, so we can write the equation:

L = 3W

We also know that the perimeter of a rectangle is given by the equation:

Perimeter = 2L + 2W

Substituting the value of L from the first equation into the second equation, we can write:

86 = 2(3W) + 2W

Now we can solve the equation for W:

86 = 6W + 2W
86 = 8W
W = 86/8
W = 10.75

Substituting the value of W back into the equation L = 3W, we can find the length:

L = 3(10.75)
L = 32.25

Therefore, the dimensions of the rectangle are 32.25 cm for the length and 10.75 cm for the width.