Answer:
[tex]l = \boxed{167.}\\w=\boxed{40.}[/tex]
Step-by-step explanation:
Since the perimeter is 414 meters, half of the perimeter is 207 meters. We can write the following equation and solve for h.
[tex]w + l = 207\\w + (4w + 7) = 207\\5w +7 = 207\\5w = 200\\w = \boxed{40.}[/tex]
Here, we substituted 4w + 7 in place of l as the problem tells us that the length of the pool is 7 meters more than 4 times the width. Solving for the width gave us 40 meters.
Using this information, we can determine that the length of the swimming pool is:
[tex]4(40) + 7 = 160 + 7 = 167.[/tex]
To double-check that this is correct, we can add twice the length and twice the width to see if it equals the given perimeter:
[tex]167 + 167 + 40 + 40 = 414.[/tex]
Therefore, your length and width of this swimming pool are:
[tex]l = \boxed{167.}\\w=\boxed{40.}[/tex]
