Question

a square lawn is surrounded by a path 2.5m wide. if area of the path is 165 m sq, find the area of the lawn.

Answer 1

let the side of the lawn be x m.

and , side of path given that 2.5m

now side of the lawn including path = x+2.5+2.5 = x+5m

now ,

we know that area of square = side²

area of lawn = area of lawn including path - area of path

now,

area of lawn = (x+5)²-165

x² = x²+25+10x - 165

x² = x²+10x-140

-10x = -140

x = 14m

now area of lawn = x²

x² = 14²

therefore ,

area of lawn = 196 m²

hope it helps !!!☺☺

Answer 2

Heya!!

Here's your solution!!!

Consider the side of the lawn be x

Given width of the path = 2.5m

side of the lawn including path = x+2(2.5m) = x+5m

so, area of lawn = (Area of the lawn including the path)-( area of the path)

Area of a square = (side)²

Therefore, we say :

x² = (x+5)²- 165m²
x² = (x²+10x+25) - 165m²
x² = x²+10x+25-165
x² = x²-10x - 140
x² - 140 = x²-10x
x²-x²-140 = -10x
-140 = -10x
i.e. 140 = 10x

Therefore x = 140/10 = 14

since the side of the lawn =14m
The area of the lawn = (14)² or 196m²

Glad help you
it helps you,
thank you ☻
@vaibhavhoax