Question

A pathway 2 meter wide runs outside a rectangular laws. The laws in 24 meter long and 16 meter broad. What is the area of the path ?

Answer 1

Answer :

• The area of the path is 196 m²

Explanation :

Given :

• Length of the lawn, L = 24 m.
• Breadth of the lawn, B = 16 m.
• Width of the lawn, w = 2 m.

To find :

• Area of the lawn, A' = ?

Knowledge required :

Formula for area of a Rectangle :

⠀⠀⠀⠀⠀⠀⠀⠀⠀A = lb

Where,

• A = Area of the rectangle
• l = Length of the rectangle
• b = Breadth of the rectangle

Solution :

First let us find the length and breadth of the rectangular lawn including the path.

• Length of the lawn including the path = Length of the lawn + 2(width of the path)

⠀⠀⠀⠀=> L' = L + 2(w)

⠀⠀⠀⠀=> L' = 24 + 2(2)

⠀⠀⠀⠀=> L' = 24 + 4

⠀⠀⠀⠀=> L' = 28

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ L' = 28 m

Hence the length of the rectangular lawn including the path is 28 m.

• Breadth of the lawn including the path = Breadth of the lawn + 2(width of the path)

⠀⠀⠀⠀=> B' = B + 2(w)

⠀⠀⠀⠀=> B' = 16 + 2(2)

⠀⠀⠀⠀=> B' = 16 + 4

⠀⠀⠀⠀=> B' = 20

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ B' = 20 m

Hence the breadth of the rectangular lawn including the path is 20 m.

Now let us find the area of the lawn and the area of the lawn including the path.

• Area of the lawn :

By using the formula for area of a Rectangle and substituting the values in it, we get :

⠀⠀⠀⠀=> A = lb

⠀⠀⠀⠀=> A = 24 × 16

⠀⠀⠀⠀=> A = 384

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ A = 384 m²

Hence the area of the lawn is 384 m².

• Area of the lawn including the path :

By using the formula for area of a Rectangle and substituting the values in it, we get :

⠀⠀⠀⠀=> A = lb

⠀⠀⠀⠀=> A = 28 × 20

⠀⠀⠀⠀=> A = 560

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ A = 560 m²

Hence the area of the lawn including the path is 560 m².

According to the question, we have to find out the area of the path, and we know the area of lawn and area of the lawn including the path.

Hence,

∴ Area of the path = Area of the lawn including the path - Area of the lawn

By substituting the values in the above equation, we get :

⠀⠀⠀⠀⠀=> A' = 580 - 384

⠀⠀⠀⠀⠀=> A' = 196

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ A = 196 m²

Therefore,

• Area of the lawn, A' =196 m².

Answer 2

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

A pathway 2 meter wide runs outside a rectangular laws. The laws in 24 meter long and 16 meter broad. What is the area of the path ?

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

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

• Lawn is 24 m long means Length of lawn = 24 m.

• Lawn is 16 m broad means breadth of lawn = 16 m.

• Breadth of pathway that run outside a rectangular law = 2 m.

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

• Area of the path.

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

• Area of the path = 196 m².

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

◖ Firstly let us find the length and breadth of the Rectangular lawn including the patth.

Length of Rectangular lawn including path ↓

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

$\large\gray{\texttt{Using formula is given below}}$

◕ Length of the lawn including the path = Length of the lawn + 2(Breadth of the path).

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

$\mapsto$ Length of lawn including the path = L + 2(b)

$\mapsto$ Length of lawn including the path = 24 + 2(2)

$\mapsto$ Length of lawn including the path = 24 + 4

$\mapsto$ Length of lawn including the path = 28 m

$\large\underbrace\mathfrak\red{Hence, \: l \: = \: 28 \: m}$

Breadth of Rectangular lawn including path ↓

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

$\large\gray{\texttt{Using formula is given below}}$

◕ Breadth of the lawn including the path = Breadth of the lawn + 2(Breadth of the path).

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

$\mapsto$ Breadth of lawn including the path = B + 2(b)

$\mapsto$ Length of lawn including the path = 16 + 2(2)

$\mapsto$ Length of lawn including the path = 16 + 4

$\mapsto$ Length of lawn including the path = 20 m

$\large\underbrace\mathfrak\red{Hence, \: b \: = \: 20 \: m}$

◖ Now let us find the area of the lawn and the area of the lawn including the path

Area of the lawn ↓

$\large\gray{\texttt{Using formula is given below}}$

$\large\gray{\texttt{Area of Rectangle formula}}$

◕ Area of Rectangle = L × B

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

$\mapsto$ A = L × B

$\mapsto$ A = 24 × 16

$\mapsto$ A = 384 m²

$\large\underbrace\mathfrak\red{Hence, \: a \: of \: lawn \: = \: 384 \: m²}$

Area of lawn including the path ↓

$\large\gray{\texttt{Using formula is given below}}$

$\large\gray{\texttt{Area of Rectangle formula}}$

◕ Area of Rectangle = L × B

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

$\mapsto$ A = L × B

$\mapsto$ A = 28 × 20

$\mapsto$ A = 560 m²

$\large\underbrace\mathfrak\red{Hence, \: a \: of \: lawn \: including \: path = \: 560 \: m²}$

◖ According to the question we know that we have to find the area of the path and we know the area of the lawn and the area of the lawn including the path

$\large\gray{\texttt{Hence,}}$

$\large\gray{\texttt{We know that}}$

◕ Area of path = Area of lawn including the path - Area of the lawn.

$\large\gray{\texttt{Using formula is given above}}$

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

$\mapsto$ A = 580 - 384

$\mapsto$ A = 196 m²

$\large\underbrace\mathfrak\red{Hence, \: a \: = \: 196 \: m²}$

$\huge{\boxed{\rm{\red{Explore \: more}}}}$

$\large\purple{\texttt{Formula of area of Rectangle}}$

$\large\purple{\texttt{L × B}}$

$\large\blue{\texttt{We also write}}$

• $\large\pink{\texttt{Length as L}}$

• $\large\pink{\texttt{Breadth as B}}$

• $\large\pink{\texttt{Area as A}}$

Hope it's helpful

Thank you :)