Question

A square lawn is surrounded by a path 4 m wide around it. If the area of the path is 320 sq. metre. Find the
area of the lawn​

Answer 1

Answer:

Area of the lawn = 256

Step-by-step explanation:

Let's assume that the side of the square lawn is "x" meters.

The area of the square lawn is x^2.

The total area of the lawn and the path is (x+8)^2 (since there is a 4m path on each side of the lawn).

Therefore, the area of the path is (x+8)^2 - x^2 = 320m².

Expanding the equation, we get:

x^2 + 16x + 64 - x^2 = 320

Simplifying it further, we get:

16x = 256

x = 16m

Therefore, the side of the square lawn is 16m.

The area of the lawn is x^2 = 16^2 = 256m².

Hence, the area of the lawn is 256m².