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?
Step by step please
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.
Step 1: Define the variables:
Let's define the width of the rectangle as "w" (in centimeters).
Since the length of the rectangle is triple the width, we can define the length as "3w" (in centimeters).
Step 2: Write the system of equations:
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, the perimeter is given as 86 centimeters. So we can write the equation as:
86 = 2(3w + w)
Step 3: Simplify and solve for "w":
Let's simplify the equation:
86 = 2(4w)
86 = 8w
Divide both sides of the equation by 8:
w = 86/8
w = 10.75
Step 4: Find the length of the rectangle:
Since the length is triple the width, we can now find the length:
Length = 3w
Length = 3(10.75)
Length = 32.25
So, the width of the rectangle is 10.75 centimeters and the length is 32.25 centimeters.
To solve this problem, we need to define variables and write a system of equations. Let's start by defining our variables:
Let's say:
L = length of the rectangle
W = width of the rectangle
According to the problem, the length of the rectangle is equal to triple the width. Therefore, we can write our first equation as:
L = 3W
Next, we know that the perimeter of a rectangle is twice the sum of its length and width. In this case, the perimeter is given as 86 centimeters. So we can write our second equation as:
2(L + W) = 86
Now, we have our system of equations:
Equation 1: L = 3W
Equation 2: 2(L + W) = 86
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Substitute the value of L from equation 1 into equation 2:
2(3W + W) = 86
Simplify:
2(4W) = 86
8W = 86
Divide both sides by 8:
W = 10.75
Step 2: Substitute the value of W into equation 1 to find L:
L = 3(10.75)
L = 32.25
So, the dimensions of the rectangle are:
Length = 32.25 centimeters
Width = 10.75 centimeters
This is how you can find the dimensions of the rectangle when given the length as triple the width and the perimeter of the rectangle.