Question

A path 2 m wide surrounds a garden 20 m by 10 m. Find
(i) the area of the path, and
(ii) the cost of paving the path at 10 per m2
​

Answer 1

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have given that a path of 2m wide is surrounding around a garden Length 20m and Breadth 10m. And we have to find:

⌬ Area of the path

⌬ Cost of paving the path at rate of ₹10/m²

$\large{\boxed{\boxed{\sf How \: to \: solve \: this?}}}$

Here, F1st we calculate the length and breadth of the garden with path surrounds it. Then we calculate the area of garden with path then calculate only the area of garden and will subtract the area of garden from area of garden with path. And will got our f1st answer. Now, for finding the cost of paving the path we simply multiply it by our f1st answer(area of path) and will got our 2nd answer.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

___________________________

Given:

⁍Length of garden = 20m

⁍Breadth of garden = 10m

⁍Path surrounded by garden = 2m

Find:

◗Area of path.

◗Cost of paving the path.

Solution:

Here, Length of Garden = 20m

→ Path surrounded by it = 2m

Length of garden with path = 20 + 2 + 2

= 20 + 4 = 24m

Now, Breadth of Garden = 10m

→ Path surrounded by it = 2m

Breadth of garden with path = 10 + 2 + 2

= 10 + 4 = 14m

Now,

$\huge{\boxed{\sf Area \: of \: Garden = l \times b}}$

$\sf where \small{\begin{cases} \sf l = 20m \\ \sf b = 10m\end{cases}}$

$\pink\bigstar$ Substituting these values:

$\implies\sf Area \: of \: Garden = l \times b$

$\implies\sf Area \: of \: Garden = 20\times 10$

$\implies\sf Area \: of \: Garden = 200 {m}^{2}$

Now,

$\huge{\boxed{\sf Area \: of \: Garden \: with \: path= l \times b}}$

$\sf where \small{\begin{cases} \sf l = 24m \\ \sf b = 14m\end{cases}}$

$\red\bigstar$ Substituting these values:

$:\to\sf Area \: of \: Garden \: with \: path= l \times b$

$:\to\sf Area \: of \: Garden \: with \: path= 24\times 14$

$:\to\sf Area \: of \: Garden \: with \: path= 336 {m}^{2}$

Now,

✏Area of path = Area of garden with path- Area of garden

where,

• Area of garden with path = 336m²
• Area of garden = 200m²

$\blue\bigstar$ Substituting these values:

✒Area of path = 336 - 200

✒Area of path = 136m²

$\underline{\boxed{ \sf\therefore Area\:of\:path\:will\:be\:136m^2}}$

___________________________

Now,

✑ Cost of paving 1m² of path = ₹10

✑ Cost of paving 136m² path = 136×10 = ₹1360

$\underline{\boxed{ \sf\therefore Cost \: of \: paving\:the \: path \: is \: Rs.1360}}$