Question

A rectangular grassy plot is 112m by 78 m. It has a gravel path 2.5m wide all round it on the inside. Find the area of the path and the cost of constructing it at 2 per square meter?

Answer 1

Answer:

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A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5m wide all round it on the inside. Find the area of the path and the cost of constructing it at 2 per square meter?

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Length of Rectangular grassy plot = 112 m.

Breadth of Rectangular grassy plot = 78 m.

Width of gravel path = 2.5 m.

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Area of the path and the cost of constructing it at ₹2 per square metre.

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We know that ,

${ \dag{ \boxed{ \sf{Area \: of \: rectangle = l× b}}}}$

So,

Area of Rectangular grassy plot

$\sf{ = 112m \times 78m = 8736 {m}^{2} }$

Now,

Length of the Rectangular grassy plot left inside the gravel path

= Length of the whole grassy plot - 2(width of the path)

$\sf = 112m - 2(2.5)m$

$\sf = 112m - 5m$

$\sf = 107m$

Breadth of the Rectangular grassy plot left inside the gravel path

= Breadth of the whole grassy plot - 2(width of the path)

$\sf = 78m - 2(2.5)m$

$\sf = 78m - 5m$

$\sf = 73m$

Now,

Area of the Rectangular grassy plot left inside the gravel path

$\sf \implies107m \times 73m$

$\sf = 7811m {}^{2}$

Now,

Area of the path

$\sf = 8736m {}^{2} - 7811 {m}^{2}$

$\sf= 925m {}^{2}$

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Cost of constructing it at 2 per square meter.

$\sf = 925 \times 2$

$\sf = ₹ 1850$

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Answer 2

Measurements of rectangular plot -

Length = 126 m

Breadth = 48 m

Area = Length x Breadth = 126 m x 48 m = 6048 m²

It has a gravel path of 1.5 m wide all round it on inside.

So, Length of inside rectangle

= 126 m -  2 x 1.5 m

= 123 m

Breadth of inside rectangle

= 48 m - 2 x 1.5 m

= 45  m

Area of inside rectangle

$= Length \:\:of\:\:inside\:\:rectangle \times Breadth \:\:of\:\:inside\:\:rectangle$

$= 123 \:m\times 45\:m\\\\=5535\:m^{2}$  

The Area of gravel path is  

$= Area\:\:of\:\:outside\;\:rectangle - Area\:\:of\:\:inside\;\:rectangle\\\\=6048\:m^{2} - 5535\:m^{2} \\\\=513 \:m^{2}$

Cost of graveling the path at Rs. 5.40 / m²

= 513 m² x Rs. 5.40 / m² = RS. 2770.2

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