Question

A square lawn is surrounded by a path 2.5m wide.If the area of the path is 165m2,find the area of the lawn.

Answer 1

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Given, Width of path = 2.5 m
Area of path = 165 m²

Let the Side of Lawn be " a " .

Area of Lawn = a²

Now, If we consider that path is also a part of a new square then the side of lawn + path = a + 2(2.5) = a+5 .
It's Area = (a+5)²

From the situation,
We can say that,

Area of path =( Area of Lawn + Path) - ( Area of Lawn)

165 = (a+5)² - a²

165 = 25 + 10a

140 = 10a

a = 14m .

Therefore ,Side of Lawn = 14m.

Area of Lawn = 14² = 196m²



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Answer 2

heya mate ,,,, think here is your answer

Given ,

Area of the path = 165m^2

width of the path = 2.5m

now let

one side of the inner square to be a

then the side of the outer square is a + 2w

area of inner square = a^2

area of outer square

= (a + 2w ) ^2

= ( a^2 + (2w ^2 ) + 2 × a × 2w )

= a^2 + 4w^2 + 2 × a × 2w

area of path = area of outer square - area of inner square

= a^2 + 4w^2 + 4aw - a^2 = 165

= 4w^2 + 4aw = 165

by substituting the value of w in the equation we get

25 + 10a = 165

a = 14

so now

area of lawn = a^2 = 14 ^2 = 196m^2