Enter the correct answer in the box. The perimeter, [tex]$P$[/tex], of a rectangle is found using the formula [tex]$P=2 l+2 w$[/tex], where [tex]$l$[/tex] is the length of the rectangle and [tex]$w$[/tex] is the width of the rectangle. Solve the formula for [tex]$w$[/tex].
Answer (2)
Subtract 2 l from both sides of the equation: P − 2 l = 2 w .
Divide both sides by 2: w = 2 P − 2 l .
Simplify the equation: w = 2 P − l .
The formula for w 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 l is the length and w is the width. Our goal is to solve this formula for w , which means we want 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 isolate the term with w : 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
Rewriting the equation We can also rewrite the equation as: w = 2 P − 2 2 l w = 2 P − l
Final Answer Therefore, the formula for w in terms of P and l is: w = 2 P − 2 l or w = 2 P − l Both forms are correct and equivalent.
Examples
Imagine you're designing a rectangular garden and you know the total length of fencing you have (the perimeter) and how long you want one side to be (the length). Solving the perimeter formula for the width allows you to calculate how wide the garden can be to use all your fencing efficiently. For example, if you have 30 meters of fencing and want the garden to be 10 meters long, you can calculate the width as follows: w = 2 P − 2 l = 2 30 − 2 ( 10 ) = 2 30 − 20 = 2 10 = 5 So, the width of the garden would be 5 meters.
To solve for the width w in the perimeter formula P = 2 l + 2 w , first subtract 2 l to get P − 2 l = 2 w , then divide by 2 to find w = 2 P − 2 l . You can also express it as w = 2 P − l which is equivalent. Both forms allow you to calculate the width of a rectangle based on its perimeter and length.
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