Question

A rectangular plot of land has length 35 m and breadth 25 m. There is a path of uniform
width 1.5 m, all around outside the plot. Find the area of the path.

Please help me ​

Answer 1

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

Here, we have given that there is a rectangular plot of land with measure of its length and breadth and there is a path surrounded outside of the plot and we have to find the area of the path.

$\large{\boxed{\boxed{\textsf{How To Do It?}}}}$

Here, F1st we calculate the total length and breadth of the rectangular plot including the path which is made around it then we will apply the formula of area of rectangle for the plot and then for the plot with path and then substituting values in it we will obtain area of plot and area of plot with path then subtracting area of plot from area of plot with path we get the area of path which is our required answer.

Let's Do It ⚡

___________________________

Given:-

▪️ Length of Rectangular plot = 35m

▪️ Breadth of Rectangular plot = 25m

▪️Path surrounded by plot = 1.5m

Find:-

▫️Area of the path

Diagram:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(1,1)(3,0){2}{\line(0,1){1}}\multiput(1,1)(0,1){2}{\line(1,0){3}}\multiput(0,2)(0.2,0){5}{\line(1,0){0.1}}\multiput(4.1,2)(0.2,0){5}{\line(1,0){0.1}}\put(2.2,2.1){\bf 35m}\put(0.2,1.4){\bf 25m}\put(0.1,2.1){\bf 1.5m}\put(4.1,2.1){\bf 1.5m} \end{picture}$

$\underline{\pink{\textsf{Note:}}}$ See diagram from Website.

Solution:-

→Length of plot = 35m

→Path surrounded by plot = 1.5m

➡ Length of plot with path = 35+1.5+1.5 = 35 + 3 = 38m

→Breadth of plot = 25m

→Path surrounded by plot = 1.5m

➡ Breadth of plot with path = 25+1.5+1.5 = 25 + 3 = 28m

Now, using

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

$\implies\sf Area_{plot}= l \times b$

$\sf where \small{\begin{cases} \sf l = 35m \\ \sf b = 25m\end{cases}}$

$\pink\bigstar$ Substituting these values:

$\mathsf{:\implies\sf Area_{plot}= l \times b}$

$\mathsf{:\implies\sf Area_{plot}= 35 \times 25}$

$\mathsf{:\implies\sf Area_{plot}= 875 {m}^{2} }$

$\begin{lgathered}\qquad\end{lgathered}$ __________________

Now, again using

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

$\implies\sf Area_{plot \: with \: path}= l \times b$

$\sf where \small{\begin{cases} \sf l = 38m \\ \sf b = 28m\end{cases}}$

$\red\bigstar$ Substituting these values:

$\dashrightarrow\sf Area_{plot \: with \: path}= l \times b$

$\dashrightarrow\sf Area_{plot \: with \: path}=38\times 28$

$\dashrightarrow\sf Area_{plot \: with \: path}=1064 {m}^{2}$

$\begin{lgathered}\qquad\end{lgathered}$ __________________

Now,

⏭ Area of the path = Area of plot with path - Area of plot

$\sf where \small{\begin{cases} \sf Area \: of \: plot = 875 {m}^{2} \\ \sf Area \: of \: plot \: with \: path = 1064 {m}^{2} \end{cases}}$

$\blue\bigstar$ Substituting these values:

▪ Area of the path = 1064 - 875

▪ Area of the path = 189m²

$\large{ \underline{\boxed{\sf \therefore Area \: of \: the \: path = 189m^2}}}$

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

A rectangular plot of land has length 35 m and breadth 25 m. There is a path of uniform width 1.5 m, all around outside the plot. Find the area of the path.

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large{\boxed{\sf{Given \: that}}}$

• Length of Rectangular plot = 35 m.

• Breadth of Rectangular plot = 25 m.

• Width of path = 1.5 m all around the plot.

$\large{\boxed{\sf{To \: find}}}$

• Area of the path.

$\large{\boxed{\sf{Solution}}}$

• Area of the path = 189 m²

$\large{\boxed{\sf{What \: the \: question \: says \: ?}}}$

$\large{\boxed{\sf{Let's \: know \: it \: 1^{st}}}}$

• The question state that there is a Rectangular plot. It's length and breadth are given , 35 metres and 25 metres. Next it say that there a path of 1.5 metre in breadth , and it is spread all around the Rectangular path. And at the last it say that we have to find the area of the path that is outside the Rectangular plot.

$\large{\boxed{\sf{Procedure \: of \: given \: question}}}$

• In this question firstly we have to calculate the length and the breadth of the plot including the path. Now using the formula of area of rectangle we have to calculate the area of plot. Now using the formula of Rectangle again we have to calculate the area of plot with path. Now we have to use the formula of area of path we will find the answer of this question.

$\large{\boxed{\sf{We \: also \: write}}}$

↝ Length as L

↝ Breadth as B

↝ Area as A

$\large{\boxed{\sf{Full \: solution}}}$

↝ L of the plot = 35 m

↝ B of path = 1.5 m

↝ L of plot with the path = 35 + 1.5 + 1.5

↝ L of plot with the path = 35 + 3

↝ L of plot with the path = 38 metres

$\bold{\pink{\fbox{\red{Hence, the l of plot with path = 38 m}}}}$

↝ B of plot = 25 metres

↝ B of path surrounded by the plot = 1.5m

↝ B of plot with the path = 25 + 1.5 + 1.5

↝ B of plot with the path = 25 + 3

↝ B of plot with the path = 28 metres

$\bold{\pink{\fbox{\red{Hence, the b of plot with path = 28 m}}}}$

$\large\purple{\texttt{Now what to do ?}}$

$\large\purple{\texttt{See below}}$

$\large\purple{\texttt{Let's carry on}}$

$\large\purple{\texttt{See the given formula}}$

$\large\underbrace\mathfrak\blue{Area \: of \: rectangle \: = \: Length \: × \: Breadth}$

Hence, we know that formula of area of rectangle is Length × Breadth

So, area of plot is Length × Breadth

↝ Area of plot = 35 × 25 {Given}

↝ Area of plot = 875 m²

$\bold{\pink{\fbox{\red{Hence, area of plot will be 875 m²}}}}$

$\large\purple{\texttt{Now what to do ?}}$

$\large\purple{\texttt{See below}}$

$\large\purple{\texttt{Let's carry on}}$

$\large\purple{\texttt{See the given formula again}}$

$\large\underbrace\mathfrak\blue{Area \: of \: rectangle \: = \: Length \: × \: Breadth}$

Hence, we know that formula of area of rectangle is Length × Breadth

So, area of plot with path

↝ Area of plot with path = 38 × 28 {Find}

↝ Area of plot with path = 1064 m²

$\bold{\pink{\fbox{\red{Hence, area of plot with path will be 1064 m²}}}}$

$\large\purple{\texttt{Now what to do ?}}$

$\large\purple{\texttt{See below}}$

$\large\purple{\texttt{Let's carry on}}$

$\large\purple{\texttt{According to the question}}$

$\large\purple{\texttt{See the formula to find A of path}}$

☃ Area of the path = Area of plot with path - Area of plot.

$\large\blue{\texttt{Here the values are}}$

$\large\orange{\texttt{Area of plot with path = 1064 m²}}$

$\large\orange{\texttt{Area of plot = 875 m²}}$

$\large\purple{\texttt{Substituting the value we get}}$

↝ Area of path = 1064 - 875

↝ Area of path = 189 m²

$\bold{\pink{\fbox{\red{Hence, area of path is 189 m²}}}}$

$\large\red{\texttt{Note :}}$ Slide the screen to view full answer in detail :)

Hope it's helpful

Thank you :)