Question

A square lawn is surrounded
by a 2.5 m
wide path. If area
of path is 165m^2 then find the area of lawn​

Answer 1

★ Procedure ::

• Here, in the above question, we are provided with width of the square lawn = 2.5m and the area of the path = 165 m². Firstly we'll assume the side of the lawn as x m and will calculate the area of the lawn by the formulae [area of square = side × side]. After applying this formulae, we will calculate the final result.

Let's do it !!

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Given :

• Width of the square lawn is 2.5 m
• Area of the path is 165 m²

To Find :

• Area of the lawn.

Solution ::

☯ Let each side of the square lawn be x m.

Area of path = 165 m² [Given]

★ (Area of big square) - (Area of small square) = 165 m²

As we know that,

$\star \boxed {\sf{ {Area}_{(square)} = side \: \times \: side }} \\ \\ \\ \bigstar \underline{\boldsymbol{According \: to \: the \: question:}} \\ \\ \\ \bf{\longrightarrow \: (x + 5)^2 \: - (x)^2} = 165 \: m^2 \\ \\ \\ \bf{\longrightarrow \: (x + 5) \: (x + 5) - x^2 = 165 } \\ \\ \\ \bf{\longrightarrow \: x^2 + 5 \: x \: + 25 \: - x^2 = 165} \\ \\ \\ \bf{\longrightarrow \: 10 \: x + 25 = 165} \\ \\ \\ \bf{\longrightarrow \: 10 \: x = 165 - 25} \\ \\ \\ \bf{\longrightarrow \: x = \cancel\dfrac{140}{10}} \\ \\ \\ \longrightarrow \underline{\boxed{\bf{x \: = \: 14 \: m}}} \: \pink{\bigstar}$

Now calculating,

$\bf{\longrightarrow \: Area \: of \: the \: lawn \: = (14 \: m)^2 } \\ \\ \\ \bf{\longrightarrow \: 14 \: m \times 14 \: m}\\ \\ \\ \longrightarrow \underline{\boxed{\bf{196 \: m^2}}} \: \purple{\bigstar}$

∴ Hence, area of the lawn is 196 cm².

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$\dag$ More Formulae :

» $\boxed {\sf{ {Area}_{(square)} = side \: \times \: side }}$

» $\boxed {\sf{ {Perimeter}_{(square)} = 4 \: \times \: side }}$

» $\boxed {\sf{ {Area}_{(rectangle)} = length \: \times \: breadth }}$

» $\boxed {\sf{ {Perimeter}_{(rectangle)} = 2 \: \times \: (l + b) }}$