Question

I need a step by step explanation on this word problem please.

Answer 1

The total fencing needed is
`\(133√(6) \, \text{ft}.\)`

To find the total amount of fencing needed to enclose the swimming pool complex, sum up the dimensions:

1. a ft: Given
`\(a = 7√(54),\)` simplify to
`\(a = 7 * 3 * √(6) = 21√(6).\)`

2. b ft: Given
`\(b = 18√(24),\)` simplify to
`\(b = 18 * 2 * √(6) = 36√(6).\)`

3. 13√24 ft: This dimension is already simplified.

4. 10√150 ft: Simplify
`\(10√(150) = 10 * 5 * √(6) = 50√(6).\)`

Now, add up all the dimensions:

`\[21√(6) + 36√(6) + 13√(24) + 50√(6).\]`

Combine like terms:

`\[107√(6) + 13√(24).\]`

To further simplify, recognize that
`\(24 = 4 * 6,\) and \(13√(24) = 13 * 2 * √(6) = 26√(6).\)`

So, the total fencing needed is
`\(107√(6) + 26√(6) = 133√(6).\)`

Therefore, the simplified answer is
`\(133√(6) \, \text{ft}.\)`

The probable question may be:

Find the number of fencing needed to enclose the swimming pool complex shown below is a=7\sqrt{54} and b=18\sqrt{24}. simplify your answer completely

The dimensions are a ft, b ft , 13\sqrt{24} ft, 10\sqrt{150}