Question

A path of uniform width 2m runs inside a square field. If the area of this path is 416 square meter. find the area of the feild which is surrounded by this path?

Answer 1

Answer:

hi plzzzzzzzzz heart me plzzzzzzzzz

Answer 2

The area of the field would be 2916 m²

Step-by-step explanation:

Let a be the side length( in meters ) of the square field,

∵ The square field is surrounded by a path of uniform width 2m runs inside it. ( shown in the below diagram )

So, the area of the path = area of field - area of field excluded the path

$=a^2-(a-4)^2$

$=a^2 - a^2 - 16 + 8a$

$=8a-16$

Note : area of a square = side²

According to the question,

8a-16 = 416

8a = 432

⇒ a = $\frac{432}{8}$ = 54 meters,

Hence, the area of the field = $54^2$ = 2916 m²

#Learn more:

The Perimeter of a square field is 64m.  If the field is surrounded by

a running path of width 3.5m. find the area of the path​...

https://brainly.in/question/10893994