Question

a square lawn is surrounded by 4m wide path around it . if the area of the path is 320 square metre . find the area of lawn.

Answer 1

let the square side be x
side of square path formed will become x+4
..area of path will give the value of x
put it into the squares side and find the squares area

Answer 2

It's a square so, the length of path inside would be equal to that of square's
So, ar of of path = ar of big square -ar of small square
Side of big square = x(let)
Side of small square = x-4-4=x-8
So, 320=x²-(x-8)²
320=x²-(x²+64-16x)
320=x²-x²-64+16x
320+64/16=x
x=24
Now side of small square = 24-8=16
So area of small square i. e. Lawn =16²=256m²