Sure, let's go step-by-step through the problem:
1. Identify the Given Information:
- We know the perimeter of the rectangular pool is 154 meters.
- The length of the pool is 2 meters more than twice its width.
2. Set Up the Variables:
- Let the width of the rectangular pool be denoted as [tex]\( w \)[/tex].
- According to the problem, the length [tex]\( l \)[/tex] of the pool can be expressed as:
[tex]\[
l = 2 + 2w
\][/tex]
3. Understand the Perimeter Formula:
- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[
P = 2(l + w)
\][/tex]
- Given that the perimeter [tex]\( P \)[/tex] is 154 meters, we can substitute the known values into the formula:
[tex]\[
154 = 2(l + w)
\][/tex]
4. Substitute the Expression for Length:
- Plug the expression for length [tex]\( l = 2 + 2w \)[/tex] into the perimeter equation:
[tex]\[
154 = 2((2 + 2w) + w)
\][/tex]
5. Simplify and Solve for [tex]\( w \)[/tex]:
- Combine like terms inside the parentheses:
[tex]\[
154 = 2(2 + 3w)
\][/tex]
- Distribute the 2:
[tex]\[
154 = 4 + 6w
\][/tex]
- Move 4 to the other side of the equation:
[tex]\[
154 - 4 = 6w
\][/tex]
[tex]\[
150 = 6w
\][/tex]
- Solve for [tex]\( w \)[/tex]:
[tex]\[
w = \frac{150}{6}
\][/tex]
[tex]\[
w = 25
\][/tex]
6. Find the Length Using the Width:
- Now that we have the width [tex]\( w \)[/tex], we substitute it back into the expression for length:
[tex]\[
l = 2 + 2w
\][/tex]
[tex]\[
l = 2 + 2(25)
\][/tex]
[tex]\[
l = 2 + 50
\][/tex]
[tex]\[
l = 52
\][/tex]
7. State the Final Answer:
- The width of the pool is 25 meters.
- The length of the pool is 52 meters.
Hence, the dimensions of the pool are:
- Width: 25 meters
- Length: 52 meters
