Question

Find the area of a square lawn whose perimeter is 72 m. Also find the cost of preparing
a flower bed in the lawn at the rate of Rs 16 per sq m.​

Answer 1

Given thαt,

• The perimeter(=length of the boundary) of a square lawn = 72m
• Cost of preparing a flower bed in the lawn = Rs 16 per m².

◾️We need to find the area of the square lawn and the cost of preparing a flower bed.

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Knowledge Required —

• $\large\star{\boxed{\bf{\orange{Perimeter_{(square)} = 4\times side}}}}\star$
• $\large\star{\boxed{\bf{\orange{Area_{(square)} = (side)^{2}}}}}\star$

To do so,

We have to find the side first.

Let's assume that side be a.

According to the question,

$\longrightarrow{\sf{4a=72m}}$

• Transpose 4 to R.H.S.

$\longrightarrow{\sf{a = \dfrac{72}{4}}}$

• Cancel out the numbers and simplify.

$\longrightarrow{\sf{a = \dfrac{\cancel{72}}{\cancel{4}}}}$

${:}\implies{\boxed{\mathbf{\pink{a(side) = 18m}}}}$

• Substitute the values in the formulae of area.

$\longrightarrow{\sf{a^{2} = 18^{2}}}$

$\longrightarrow{\sf{18\times18}}$

$\large{:}\implies{\boxed{\mathbf{\red{324m^{2}}}}}$

Therefore, the area is 324m².

Cost of preparing a flower bed = Area of the square lawn*Cost.

• Substitute the values.

$\longrightarrow{\sf{324\times16}}$

$\large{:}\implies{\boxed{\mathbf{\red{Rs.5,184}}}}$

Hence, the cost of preparing a flower bed in the square lawn is Rs. 5,184.

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