Question
Problem Solving (Reol world The formula \( P=2 \ell+2 w \) gives the perimeter \( P \) of a rectangular room with length \( \ell \) and width \( w \). A rectangular living room is 26 feet long and 21 feet wide. What is the perimeter of the room?
Ask by Hampton Carter. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The perimeter of the room is 94 feet.
Solution
We are given that the perimeter \( P \) of a rectangle is given by
\[
P = 2\ell + 2w
\]
where \( \ell \) is the length and \( w \) is the width. For this problem, the length \( \ell \) is 26 feet and the width \( w \) is 21 feet.
1. Substitute the given values into the formula:
\[
P = 2(26) + 2(21)
\]
2. Perform the multiplications:
\[
P = 52 + 42
\]
3. Add the two results to find the perimeter:
\[
P = 94
\]
Thus, the perimeter of the room is \( 94 \) feet.
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Simplify this solution The Deep Dive
To find the perimeter of the living room using the formula \( P = 2\ell + 2w \), simply substitute the given values: \( \ell = 26 \) feet and \( w = 21 \) feet. Plugging these into the formula gives: \[ P = 2(26) + 2(21) = 52 + 42 = 94 \] So, the perimeter of the living room is 94 feet! When working with formulas like this one, it’s easy to make a common mistake: forgetting to multiply both length and width by 2. Always double-check your multiplication to ensure you’re not missing those crucial steps—otherwise, you might end up with a perimeter that’s way off!
