Question

A square garden has a 2 m wide path surrounding it. If the area of the path is
136 m 2, find the area of the garden

Answer 1

Answer:

Let ABCD be the square lawn and PQRS be the outer boundary of the square path. Let side of the lawn AB be x m. Area of the square lawn = x2 Given that Length PQ = (x + 2 + 2) = (x + 4) m Area of PQRS = (x + 4)2 = (x2 + 8x + 16) m2 Now, Area of the path = Area of PQRS – Area of the square lawn 136 = x2 + 8x + 16 – x2 136 = 8x + 16 136 – 16 = 8x 120 = 8x x = 120/ 8 = 15 Side of the lawn = 15 m Hence, Area of the lawn = (Side)2 = (15 m)2 = 225 m2Read more on Sarthaks.com - https://www.sarthaks.com/690355/square-lawn-has-wide-path-surrounding-if-the-area-of-the-path-is-136-find-the-area-of-the-lawn