The formula $P=2l+2w$ means that the perimeter of a rectangle is equal to twice the sum of its length and its width.
Solve $P=2l+2w$ for $w$.
A. $w=P-2-l$
B. $w=\frac{P-2 l}{2}$
C. $w=\frac{P-2 l}{2}$
D. $w=\frac{P-2}{l}
Answer (2)
Subtract 2 l from both sides of the equation: P − 2 l = 2 w .
Divide both sides by 2 to isolate w : w = 2 P − 2 l .
The solution for w is 2 P − 2 l .
Therefore, the answer is w = 2 P − 2 l .
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 w on one side of the equation.
Isolating the term with w First, we subtract 2 l from both sides of the equation to get: P − 2 l = 2 l + 2 w − 2 l P − 2 l = 2 w
Solving for w Next, we divide both sides of the equation by 2 to solve for w : 2 P − 2 l = 2 2 w w = 2 P − 2 l
Final Answer Therefore, the solution is w = 2 P − 2 l , which corresponds to option C.
Examples
Understanding how to rearrange formulas is crucial in many real-world applications. For example, if you're designing a rectangular garden with a specific perimeter and you know the length, you can use this rearranged formula to determine the required width. This ensures you maximize the garden's area within the given perimeter constraints. Similarly, in construction or interior design, rearranging formulas helps in calculating dimensions to fit specific requirements and optimize space utilization.
To isolate w in the formula P = 2 l + 2 w , we first subtract 2 l from both sides to get P − 2 l = 2 w , and then divide by 2 to solve for w as w = 2 P − 2 l . The correct multiple choice option is C.
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