3. 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.
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.
Let's define the variables:
Let L = length of the rectangle
Let W = width of the rectangle
We are given that the length of the rectangle is equal to triple the width, so we can write the equation:
L = 3W
We are also given that the perimeter of the rectangle is 86 centimeters. The formula for the perimeter of a rectangle is:
Perimeter = 2(L + W)
Substituting the equation for L, we have:
86 = 2(3W + W)
Simplifying:
86 = 2(4W)
86 = 8W
Dividing both sides by 8:
10.75 = W
The width of the rectangle is 10.75 centimeters.
Substituting this value back into the equation for L, we have:
L = 3(10.75)
L = 32.25
The length of the rectangle is 32.25 centimeters.
So, the dimensions of the rectangle are:
Length = 32.25 cm
Width = 10.75 cm
To solve this problem, let's define the variables and write the system of equations.
Let's denote the width of the rectangle as 'w' centimeters.
According to the problem, the length of the rectangle is equal to triple the width. So, the length can be represented as '3w' centimeters.
The perimeter of a rectangle is given by the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In our case, the perimeter is given as 86 centimeters. So, the equation becomes:
86 = 2(3w + w)
Now, simplify the equation:
86 = 2(4w)
Divide both sides of the equation by 2:
43 = 4w
Now, divide both sides of the equation by 4 to solve for 'w':
w = 43/4
So, the width of the rectangle is 10.75 centimeters.
To find the length, substitute the value of 'w' into the expression for the length:
Length = 3w = 3 * 10.75 = 32.25 centimeters
Therefore, the dimensions of the rectangle are width = 10.75 centimeters and length = 32.25 centimeters.
In summary, the system of equations that can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters is:
w = 43/4
Length = 3w = 3 * (43/4) = 32.25 cm