To determine the width of the rectangular house, we need to follow a systematic approach to solve the problem.
1. Convert the given perimeter from yards to feet.
- The given perimeter of the house is [tex]\( 25^{1/3} \)[/tex] yards.
- Since 1 yard is equivalent to 3 feet, we can convert the perimeter to feet by multiplying:
[tex]\[
\text{Perimeter in feet} = 25^{1/3} \times 3
\][/tex]
This results in approximately 8.772 feet.
2. Understand the relationship between the perimeter, length, and width of the rectangle.
- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[
P = 2 \times \text{Length} + 2 \times \text{Width}
\][/tex]
- We already know the length [tex]\( L \)[/tex] is 22 feet, and we have the perimeter [tex]\( P \)[/tex] in feet.
3. Rearrange the perimeter formula to solve for the width [tex]\( W \)[/tex]:
- Subtract twice the length from the perimeter:
[tex]\[
2 \times \text{Width} = \text{Perimeter} - 2 \times \text{Length}
\][/tex]
- Substitute the given length and calculated perimeter:
[tex]\[
2 \times \text{Width} = 8.772 - 2 \times 22
\][/tex]
[tex]\[
2 \times \text{Width} = 8.772 - 44
\][/tex]
[tex]\[
2 \times \text{Width} = -35.228
\][/tex]
4. Solve for the width [tex]\( W \)[/tex]:
- Divide both sides by 2:
[tex]\[
\text{Width} = \frac{-35.228}{2}
\][/tex]
[tex]\[
\text{Width} = -17.614
\][/tex]
Thus, the calculated width of the rectangular house is approximately [tex]\( -17.614 \)[/tex] feet. However, since width cannot be negative in a real-world context, there might be an issue with the given values or a misunderstanding in the problem setup.
In the context of the multiple choice answers provided:
1. 16 feet
2. 35 feet
3. 37 feet
4. 40 feet
5. 42 feet
None of these choices match the calculated width. Review the problem data or consult for any clarification would be recommended as subsequent steps.
