Select the correct answer.
Given the following formula, solve for [tex]$l$[/tex].
[tex]$P=2(l+b)$[/tex]
A. [tex]$l=4(P+b)$[/tex]
B. [tex]$l=\frac{P-2 b}{2}$[/tex]
C. [tex]$l=\frac{P-b}{2}$[/tex]
D. [tex]$l=\frac{P-b}{4}$[/tex]
Answer (2)
Divide both sides of the equation by 2: 2 P = l + b .
Subtract b from both sides: 2 P − b = l .
Rewrite with a common denominator: l = 2 P − 2 b .
The solution for l is: l = 2 P − 2 b .
Explanation
Understanding the Problem We are given the formula P = 2 ( l + b ) and asked to solve for l . This means we want to isolate l on one side of the equation.
Dividing by 2 First, we divide both sides of the equation by 2 to get rid of the coefficient 2 on the right side: 2 P = 2 2 ( l + b ) 2 P = l + b
Subtracting b Next, we subtract b from both sides of the equation to isolate l :
2 P − b = l + b − b 2 P − b = l
Finding a Common Denominator To express the result as a single fraction, we find a common denominator for the left side of the equation. The common denominator is 2: l = 2 P − 2 2 b l = 2 P − 2 b
Final Answer Therefore, the solution for l is: l = 2 P − 2 b
Examples
This formula and its rearrangement can be used in various real-life scenarios. For example, if you're designing a rectangular garden with a known perimeter and width, you can use this formula to determine the length needed. Similarly, if you're framing a picture and know the perimeter and the width of the frame, you can calculate the length required. This type of algebraic manipulation is essential for solving practical problems involving geometric shapes and measurements.
To solve for l in the equation P = 2 ( l + b ) , we isolate l by dividing by 2 and subtracting b . This leads us to the final solution l = 2 P − 2 b , which corresponds to option B.
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