Around a square pool, there is a footpath of width `2m`. If the area of the foothpath is `5/4` times that of the pool, find the area of the pool.

Explanation

Let the length of the square pool be `x` m.
Then the length of the footpath is
`(x+2+2)=(x+4)m`
The area of the footpath
`=` the area of the outer square `-` the area of the pool
`:.` The area of the foothpath `=(x+4)^(2)-x^(2)`
From the given condition
`(x+4)^(2)-x^(2)=5/4 x^(2)`
`:.x^(2)+8x+16-x^(2)-5/4x^(2)`
`:.8x+16=6/4x^(2)`
`:.32x+64=5x^(2)` .....(Multiplying both the sides by 4)
`:.5x^(2)-32x-64=0`

`:.5x^(2)-40x+8x-64=0`
`:.5x(x-8)+(x-8)=0`
`:.(x-8)(5x+8)=0`
`:.x-8-0` or `5x+8=0`
`:.x=8` or `x=-8/5`
But the length cannot be negative.
`:.x=-8/5` is unacceptable
`:.x=8` The area of the pool `=x^(2)=(8)^(2)=64m^(2)`
Ans. The area of the pool is `64m^(2)`