Question
Solve the following for the indicated variable: \( A=l w \) for \( l \) \( l=\square \)
Ask by Salinas Mcfarlane. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( l = \frac{A}{w} \)
Solution
Solve the equation \( A=lw \) for \( l \).
Solve the equation by following steps:
- step0: Solve for \(l\):
\(A=lw\)
- step1: Rewrite the expression:
\(A=wl\)
- step2: Swap the sides:
\(wl=A\)
- step3: Divide both sides:
\(\frac{wl}{w}=\frac{A}{w}\)
- step4: Divide the numbers:
\(l=\frac{A}{w}\)
The solution to the equation \( A = lw \) for \( l \) is \( l = \frac{A}{w} \).
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Simplify this solution The Deep Dive
To solve for \( l \) in the equation \( A = lw \), we need to isolate \( l \). We can do this by dividing both sides of the equation by \( w \) (assuming \( w \neq 0 \)): \[ l = \frac{A}{w} \] So now we have \( l = \frac{A}{w} \). This relationship shows that the length \( l \) is determined by the area \( A \) and the width \( w \). Now, if you're looking to understand how this formula can be applied in real life, consider this: if you’re designing a garden plot or a room, measuring the area and knowing the width can help you figure out the necessary length of the space. This can save you materials and cash while ensuring everything fits just right!
