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.
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=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))`
`= 66 m^2`
or `A= 4(2)^2 - 50(2)+150`
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`