Question

18. A square lawn is surrounded by a path 2.5 m wide. If the area of path
is 165 m2. Find the area of lawn.​

Answer 1

The area of the lawn is 196 m²

Step-by-step explanation:

Given :

Width of the path surrounding the square lawn = 2.5 m

Area of the path = 165 $\text{m}^{2}$

Consider a be the side of the square lawn

Side of the lawn including path area = a + 2(2.5) m = a + 5 m

Area of the square = $\text{side}^{2}$

Area of the lawn including path = $(\text{a}+5)^{2}$

Area of the lawn = $\text{a}^{2}$

Area of the square lawn = Area of the square lawn including path - area of the path

$\text{a}^{2} = (\text{a}+5)^{2} - 165 \\\\\text{a}^{2} = \text{a}^{2}+10\text{a} + 25 - 165 \\\\\text{a}^{2} = \text{a}^{2}+10\text{a} -140\\\\ \text{a}^{2} -140 = \text{a}^{2}+10\text{a}$

$\text{a}^{2} -\text{a}^{2} - 140 = 10\text{a}\\\\10 \text{a} = 140\\\\\text{a} = \frac{140}{10} = 14$

∴ Area of the lawn = $(14)^{2} = 196 \text{m}^{2}$

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