the length of a rectangle is 4cm less then twice its width. the perimeter of the rectangle is 34cm. what are the demensions of the rectangle?
To find the dimensions of the rectangle, we can follow these steps:
Step 1: Assign variables
Let's assign variables to represent the width and length of the rectangle.
Let's say:
Width = W
Length = L
Step 2: Set up equations
Based on the given information, we can set up two equations.
Equation 1: "The length of a rectangle is 4cm less than twice its width."
L = 2W - 4
Equation 2: "The perimeter of the rectangle is 34cm."
Perimeter = 2(L + W)
34 = 2(L + W)
Step 3: Solve the system of equations
Now we will substitute the value of L from Equation 1 into Equation 2.
34 = 2((2W - 4) + W)
Now simplify and solve for W:
34 = 2(3W - 4)
34 = 6W - 8
6W = 42
W = 7
Step 4: Find the length
Now that we have the value of W, we can substitute it back into Equation 1 to find L.
L = 2W - 4
L = 2(7) - 4
L = 14 - 4
L = 10
Step 5: Check the solution
We can check our solution by substituting the values back into the perimeter equation (Equation 2):
Perimeter = 2(L + W)
34 = 2(10 + 7)
34 = 2(17)
34 = 34
The perimeter is indeed 34, so our solution is correct.
Therefore, the dimensions of the rectangle are:
Width = 7 cm
Length = 10 cm