Select the correct answer.
Given the following formula, solve for $l$.
$P=2(l+b)$
A. $l=\frac{P-2 b}{2}$
B. $l=4(P+b)$
C. $l=\frac{P-b}{4}$
D. $l=\frac{P-b}{2}$
Answer (1)
Divide both sides of the equation by 2: 2 P = l + b .
Subtract b from both sides: 2 P − b = l .
Find a common denominator: l = 2 P − 2 2 b .
Express l in terms of P and b : l = 2 P − 2 b . The final answer 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 left side as a single fraction, we find a common denominator, which is 2: l = 2 P − 2 2 b l = 2 P − 2 b
Final Answer Therefore, the correct answer is l = 2 P − 2 b , which corresponds to option A.
Examples
This formula and its rearrangement are useful in various real-life scenarios. For example, if you're designing a rectangular garden and know the total perimeter ( P ) and the width ( b ), you can use this formula to calculate the required length ( l ). This ensures you use the available space efficiently and purchase the correct amount of fencing. Knowing how to manipulate formulas allows for efficient problem-solving in design and resource management.
