The length of a rectangular park is 11 metre more than its breadth. The area of park is 242 square metre. There is a 5 metre wide path around the park. Find the area of the path.

Explanation:

Width of Park = x metre (let)

∴ Its length = (x + 11) metre

∴ x(x + 11) = 242

= 11 (11 + 11)

=> x = 11 metre = width

∴ Length = 22 metre

Length of park with path

= 22 + 2 × 5 = 32 metre = EH Width

= 11 + 2 × 5 = 21 metre = EF

∴ Area of path

= EH × EF – AB × BC

= 32 × 21 – 242

= 672 – 242 = 430 sq.metre