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

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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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$\large{ \frak{ \underline{ \red{Given :}}}}$

Length of Rectangular grassy plot = 112 m.

Breadth of Rectangular grassy plot = 78 m.

Width of gravel path = 2.5 m.

$\large{ \frak{ \underline{ \pink{To\: find :}}}}$

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

$\large{ \frak{ \underline{ \purple{Solⁿ :}}}}$

$\large{ \frak{ \underline{ \blue{1st \: part \: of \: Question}}}}$

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

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

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

$\large{ \frak{ \underline{ \color{blue}{2nd \: part \: of \: Question}}}}$

Cost of constructing it at 2 per square meter.

$\sf = 925 \times 2$

$\sf = ₹ 1850$

$\sf{ \green{Hope \: it \: helps...}}$

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Answer 2

Here is the correct answer to your question

Refer to the attachment for the details..

Hope this helps you ❤️☑️

Have a great day