Question

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

Answer 1

Let side of Square is X m

Area of Path = Area with path - Area of lawn

Area of Lawn = Area with Path - Area of Path

X^2 = { (X+5)×(X+5) } - 165

X^2 = X^2 +25 +10X -165

10X= 140

X=14 m

Area of Lawn = X^2= 14^2= 196 sq m.

$196sq \: meter$

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Side of lawn = p

Width = 2.5m

$\textbf{\underline{Side\;of\;lawn\;with\;path}}$

= p + 2 × 2.5

= p + 5

$\textbf{\underline{Area\;of\;lawn}}$

${\boxed{\sf\:{=Area\;of\;lawn\;with\;path - Area\;of\; path}}}$

Using Formula

Area of square = (a)²

p² = (p + 5)² - 165 m²

p² = p² + 5² + 2 × p × 5 - 165

p² = p² + 25 + 10p - 165

p² = p² + 10p - 140

p² - 10p = p² - 140

p² - p² - 10p = -140

-10p = -140

10p = 140

${\boxed{\sf\:{p=\dfrac{140}{10}}}}$

p = 14 m

$\textbf{\underline{Side\;of\;lawn=14\;m}}$

Hence

Area of lawn = (a)²

Area of lawn = (14)²

Area of lawn = 196 m²

$\Large{\boxed{\sf\:{Area\;of\;lawn=196 m^2}}}$