Question

A square lawn is surrounded by a path 2m wide . If the area of the path is 240msquare , find the area of the lawn
surrounded by a path 2 meter wide.If the area of the path is 240 meter square , find the area of the lawn

Answer 1

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Let the side of lawn be a m

$Area \: of \: lawn = {a}^{2}$

Length of Outer side = (a+4) m

$Area \: of \: outer \: square = {a + 4}^{2} \\ = {a}^{2} + 16 + 8a$

Area of path = Area of outer square - Area of lawn.

$240 = {a}^{2} +16 + 8 a - {a}^{2}$

=> 240 = 8a + 16

=> 8(a+2) = 240

=> a+2 = 30

=> a= 28 m

$Area \: of \: lawn = 28 \times 28</p><p>= 784 {m}^{2}$

$\huge{\underline {\mathcal{\orange{Thank You}}}}$

Answer 2

Answer:

784 m²

Step-by-step explanation:

Let us assume the area of lawn = 'a' m.

Then,

Area of square = a²

A square lawn is surrounded by a path 2 m wide.

Length of outer side = (a + 2 + 2) = (a + 4) m.

Area of outer side = (a + 4)² = a² + 8a + 16.

Also given,

Area of path is 240 m².

=> 240 = a² + 8a + 16 - a²

=> 240 = 8a + 16

=> 8a = 224

=> a = 28

Thus,

Side of lawn = 28 m

Area of lawn = s²

                     = 28 * 28

                     = 784 m²

Therefore,

area of lawn = 784 m²

Hope it helps!