Question

a foot pathof uniform width 5m runs inside of a rectangular park 38 m and 32m wide . find the area of the path​

Answer 1

Given

length of rectangular field=38m

Breadth of rectangular field=32m

and width of footpath=5m

concept

First of all calculate the area of park and subtract from area of footpath.

Solution

Area of park =

$38 \times 22 = 1216 \: {m}^{2}$

Length of footpath =

$5 \times 2 - 38 = 28$

Breadth of footpath=

$5 \times 2 - 32 = 22$

area of footpath=

$22 \times 28 = 616 {m}^{2}$

Total area of footpath inside rectangular park=

$1216 - 616 = 600 {m}^{2}$

Answer

Hope it is helpful for you

Answer 2

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

Let PQRS be the rectangular park and ABCD be the internal boundaries of the bath.

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

• Length PQ = 38 m
• Breadth QR = 32 m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 38\:m \times 32\:m}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 1216\:m^2}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Length AB = 38 m - 5m - 5m}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 28\:m}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bullet\;\;\underline{\textbf{\textsf{Length BC = 32 m - 5m - 5m}}}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 22\:m}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 28\:m \times 22\:m}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 616\:m^2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 1216\:m^2 - 616\:m^2}$

$\sf {\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 600\:m^2}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf\underline{\purple{\:\:\: \therefore Area\:of\:foothpath = 600\:m^2\:\:\:}}$

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