Question

A rectangular Garden 78 metre long and 35 metre broad has a uniform path 1 metre wide all around it on the outside find the area of the path

Answer 1

Area of ABCD =35m *78m

=2730m²

JM=35m+1+1

=37m

JK=78+1+1

=80m

Area of JKLM = length x breadth

= 37 X 80

=2960m²

area of path = area of JKLM -area of ABCD

=2960 - 2730

=230 m²

Answer 2

$\huge\bf{\underline{\purple{Solution:-}}}$

Let PQRS be the rectangular garden and ABCD be the external boundary of the path.

$\bf\underline{\red{\:\:\:\:\:\:\:\:We\: have:-\:\:\:\:\:\:\:}}$

• Length PQ = 78 m
• Breadth QR = 35 m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Area of rectangle PQRS = PQ × QR}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 78\:m \times 35\:m}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 2730\:m^2}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Length AB = 78 m + 1m + 1m}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 80\:m}$

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$\bullet\;\;\underline{\textbf{\textsf{Breadth BC = 35 m + 1m + 1m}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 37\:m}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Area of rectangle ABCD = AB × BC}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 80\:m \times 37\:m}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 2960\:m^2}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Area of path = Area of rectangle ABCD - Area of rectangle PQRS}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 2960\:m^2 - 2730\:m^2}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 230\:m^2}$

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$\sf\underline{\purple{\:\:\: \therefore Area\:of\:path = 230\:m^2\:\:\:}}$

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