Solve system of equations to model the problem then solve:
The length of a rectangle is 7 inches more than the width. The perimeter is 34 inches. Find the length and the width of the rectangle.
P = 2L + 2W
34 = 2(W + 7) + 2W
To solve this problem, we can set up a system of equations based on the given information.
Let's start by assigning variables to the unknown quantities. Let's say:
- W represents the width of the rectangle
- L represents the length of the rectangle
Based on the problem statement, we can write two equations:
1) "The length of the rectangle is 7 inches more than the width."
L = W + 7
2) "The perimeter is 34 inches."
The perimeter of a rectangle is calculated by adding up all four sides, so we can write:
2L + 2W = 34
Now we have a system of two equations:
Equation 1: L = W + 7
Equation 2: 2L + 2W = 34
To solve this system, we can use substitution or elimination method. Let's use substitution method to solve it.
Step 1: Substitute the value of L from Equation 1 into Equation 2:
2(W + 7) + 2W = 34
Step 2: Simplify the equation:
2W + 14 + 2W = 34
4W + 14 = 34
4W = 34 - 14
4W = 20
Step 3: Divide both sides of the equation by 4 to solve for W:
W = 20/4
W = 5
Step 4: Substitute the value of W back into Equation 1 to solve for L:
L = 5 + 7
L = 12
Therefore, the width of the rectangle is 5 inches and the length is 12 inches.