# The outside edge of a path around a rectangular swimming pool is 15m long and 10m wide. The path is x metres wide. a) Find an expression for the area of the pool in expanded form. b) Find the...

The outside edge of a path around a rectangular swimming pool is 15m long and 10m wide. The path is x metres wide.

a) Find an expression for the area of the pool in expanded form.

b) Find the area of the pool if x=2.

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### 1 Answer

To find the area of a rectangle:

`A = l times b` where l = length and b = breadth or width

The path around the edge of the pool is 15 m by 10 m. That means that **each** side of the pool is shorter by x meters and we must take that into consideration.

`therefore` `l -(x+x)` and `b=b-(x+x)` because we must deduct x on each side. We know that l=15m and b=10m and that `A= l times b`

`therefore A=(15-2x)(10-2x)`

`therefore A=150 -30x-20x+4x^2`

`therefore A=4x^2 - 50x +150` is the expression in expanded form

If x=2 we can substitute into any of our given expressions.

`therefore A= (15-2(2))(10-2(2))`

`therefore A=(11)(6)`

`= 66 m^2`

or `A= 4(2)^2 - 50(2)+150`

`= 16-100+150`

`= 66m^2`

**Ans: The expression for the area of the rectangular pool is** `4x^2 - 50x+150`

**and when x=2 the area of the pool is `66m^2` **