Perimeter = 216 and the length is (2X)+3 more than the width. How do I solve for X and what is the rectangle length. I am really stuck!
W = X
L = 2X + 3
216 = 2X + 2(2X+3)
Solve for X, then 2X + 3.
To solve for X and find the length of the rectangle, let's break down the problem step by step.
Step 1: Understand the problem
The problem provides us with the perimeter of a rectangle, which is 216 units. It also tells us that the length of the rectangle is (2X) + 3 more than the width. We need to find the value of X and the length of the rectangle.
Step 2: Define the variables
Let's assign variables to the dimensions of the rectangle.
Let:
- L = Length of the rectangle
- W = Width of the rectangle
- X = Value we need to find
Step 3: Formulate equations
The perimeter of a rectangle is given by the formula: 2L + 2W.
In this case, we have the perimeter as 216, so we can write the equation as:
2L + 2W = 216
We also know that the length is (2X) + 3 more than the width. So we can write:
L = W + (2X) + 3
Step 4: Simplify the equations
We have two equations:
Equation 1: 2L + 2W = 216
Equation 2: L = W + (2X) + 3
Step 5: Solve the equations
To solve for X and find the length, we need to eliminate one variable from the equations. Let's eliminate L by substituting the value of L from equation 2 into equation 1.
Replace L in equation 1 with the expression for L from equation 2:
2(W + (2X) + 3) + 2W = 216
Now simplify and solve the resulting equation for W.
Step 6: Solve for W
Distribute 2 to each term within the parentheses:
2W + 4X + 6 + 2W = 216
Combine like terms:
4W + 4X + 6 = 216
Subtract 6 from both sides of the equation:
4W + 4X = 210
Step 7: Solve for X
To solve for X, we need to isolate X on one side of the equation.
Subtract 4W from both sides of the equation:
4X = 210 - 4W
Divide both sides of the equation by 4:
X = (210 - 4W) / 4
Step 8: Find the length
To find the length, substitute the value of X into equation 2:
L = W + (2X) + 3
Substitute the value of X we found in Step 7:
L = W + (2(210 - 4W) / 4) + 3
Simplify the equation to find the length.
By following these steps, you can solve for X and find the length of the rectangle.