The formula $P=2 l+2 w$ means that the perimeter of a rectangle is equal to twice the sum of its length and its width.
Solve $P=2 l+2 w$ for $l$.
A. $I=P-2-w$
B. $I=\frac{P-2}{w}$
C. $I=\frac{P+2 w}{2}$
D. $I=\frac{P-2 W}{2}$
Answer (1)
Subtract 2 w from both sides of the equation: P − 2 w = 2 l .
Divide both sides by 2 to isolate l : l = 2 P − 2 w .
The solution for l is l = 2 P − 2 w .
Explanation
Understanding the Problem We are given the formula for the perimeter of a rectangle, P = 2 l + 2 w , where P is the perimeter, l is the length, and w is the width. Our goal is to isolate l on one side of the equation.
Isolating the Term with l First, we subtract 2 w from both sides of the equation to get: P − 2 w = 2 l + 2 w − 2 w P − 2 w = 2 l
Solving for l Next, we divide both sides of the equation by 2 to solve for l :
2 P − 2 w = 2 2 l l = 2 P − 2 w
Identifying the Correct Option Comparing our result with the given options, we see that option D matches our solution.
Final Answer Therefore, the solution is l = 2 P − 2 w .
Examples
Imagine you're designing a rectangular garden and you know the total perimeter you want and how wide you want the garden to be. Using this formula, you can calculate exactly how long the garden needs to be to meet your perimeter requirements. For example, if you want a garden with a perimeter of 30 feet and a width of 5 feet, you can calculate the length as follows: l = 2 P − 2 w = 2 30 − 2 ( 5 ) = 2 30 − 10 = 2 20 = 10 So, the length of the garden should be 10 feet.
