Question

a path of 2m side running all around a square garden has an arera of 9680m2. find the area of the part of the garden enclosed by the path

Answer 1

Step-by-step explanation:

A square field is surrounded by a path 2 m wide outside. The area of the path is 72 sqm. What is the area of the field?

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Assume side of the square field to be x metre(m).

Therefore, area of the square field=side^2 = x^2

“A square field is surrounded by a path 2 m wide outside.” So path of 2 m surrounding on both sides…..

Therefore, side of square field with path= x+2+2 =x+4

Area of square field with path=(x+4)^2

NOW WHAT EXACTLY IS THE PATH? It is:- (the total square field with path) - (square field without path)

As a result the area of the PATH is the (Area of the field with path) - (Area of the field without path)

So (x+4)^2 - x^2 =72——————————- (equation)

or, x^2 + 8x + 16 - x^2 = 72

or, 8x + 16= 72

or, 8x= 56

or x = 7 ( side of square field )

So area of sq. field= 49 sq. cm.