Question

A path of uniform width 2.5 m runs outside a rectangular plot of dimension 32 m by 18 m. Find the area of the path.​

Answer 1

Given :-

Dimensions of Inner Rectangle :

• Length of Inner Rectangle = 32m
• Breadth of Inner Rectangle = 18m
• Width of the Path = 2.5m

To Find :-

• Area of the Path.

Solution :-

Dimensions of Outer Rectangle :

★ Length of Outer Rectangle ★

Length of Outer Rectangle = Length of Inner Rectangle + Width of Path on both the sides

➟ Length = 32 + ( 2.5 + 2.5 )

➟ Length = 32 + 5

➟ Length of Outer Rectangle = 37m

★ Breadth of Outer Rectangle ★

Breadth of Outer Rectangle = Breadth of Inner Rectangle + Width of Path on both the sides

➟ Breadth = 18 + ( 2.5 + 2.5 )

➟ Breadth = 18 + 5

➟ Breadth of Outer Rectangle = 23m

________________

★ Area of Inner Rectangle ★

⇛ Area of Inner Rectangle = L × B

⇛ Area of Inner Rectangle = 32 × 18

⇛ Area of Inner Rectangle = 576m²

________________

★ Area of Outer Rectangle ★

⇛ Area of Outer Rectangle = L × B

⇛ Area of Outer Rectangle = 37 × 23

⇛ Area of Outer Rectangle = 851m²

________________

★ Area of Path ★

⮕ Area of Path = Area of Outer Rectangle - Area of Inner Rectangle

⮕ Area of Path = 851 - 576

⮕ Area of Path = 275m²

________________

Therefore, The Area of Path is 275m²

________________

Answer 2

Step-by-step explanation:

━━━━━━━━━━━━━━━━━━━━━━━━

A path of uniform width 2.5 m runs outside a rectangular plot of dimension 32 m by 18 m. Find the area of the path.

⠀━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\blue{\mathrm{Given: : }}}}$

Dimensions of Inner Rectangle

$\sf\green{Length\: of\: Inner\: Rectangle = 32m }$

$\sf\red{ Breadth \:of\: Inner \:</p><p>0Rectangle = 18m}$

$\sf\orange{ Width \:of\: the \:Path = 2.5m}$

$\huge{\underline{\red{\mathrm{To\:Find\: :}}}}$

$\sf\blue{ Area\: of \:the\: Path}$.

$\huge{\underline{\mathrm{Solution\: : }}}$

Area of Path :

$\sf\red{ Area \:of \:Path = Area\: of \:Outer\: as was Rectangle - Area \:of \:Inner \:Rectangle}$

$\sf\blue{Area \:of \:Path = 851 - 576}$

$\sf\pink{ Area \:of \:Path = 275m² }$

⠀━━━━━━━━━━━━━━━━━━━━━━━━

Therefore, The Area of Path is 275m²