The length of a rectangular swimming pool is 24m more than twice its width. The perimeter of the pool is 108m. Determine the dimensions of the pool.
P = 2L + 2W
108 - 2(2W + 24) + 2W
108 = 6W + 48
60 = 6W
10 = W
To determine the dimensions of the rectangular swimming pool, let's assign variables for the width and length. Let's say the width is "w" meters and the length is "l" meters.
According to the given information, the length of the pool is 24m more than twice its width. This can be written as:
l = 2w + 24
The perimeter of a rectangular shape is the sum of all its sides. In this case, the perimeter of the pool is 108m, so we can write the equation:
2w + 2l = 108
Now let's solve for the dimensions of the pool:
Substitute the value of "l" from the first equation into the second equation:
2w + 2(2w + 24) = 108
Simplify the equation:
2w + 4w + 48 = 108
Combine like terms:
6w + 48 = 108
Subtract 48 from both sides:
6w = 60
Divide both sides by 6:
w = 10
Now we know that the width of the pool is 10 meters.
Substitute this value back into the first equation to find the length:
l = 2w + 24
l = 2(10) + 24
l = 20 + 24
l = 44
Therefore, the dimensions of the rectangular swimming pool are 10 meters for the width and 44 meters for the length.