Question

The perimeter of a rectangular swimming pool is 414 meters. The length of the pool is 7 meters more than four times the width. Find the length and the width

Answer 1

Answer:

$l = \boxed{167.}\\w=\boxed{40.}$

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.

$w + l = 207\\w + (4w + 7) = 207\\5w +7 = 207\\5w = 200\\w = \boxed{40.}$

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:

$4(40) + 7 = 160 + 7 = 167.$

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:

$167 + 167 + 40 + 40 = 414.$

Therefore, your length and width of this swimming pool are:

$l = \boxed{167.}\\w=\boxed{40.}$