Question

A rectangular field is 120m long and 65m wide . It has two crossroads each of width 2m running in the middle of it one parts to its length and one parallel to its breadth. Find the area of tha path .

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bf{Dimensions}\begin{cases}\sf{length (l)=120m}\\ \sf{Breadth (b)=65m}\end{cases}$

$\boxed{\sf{Area\:of\: rectangle=Length\times breadth}}$

• Now to find the area of park which is parallel to length

$\bf{we\:have}\begin{cases}\sf{Length (l)=120m}\\ \sf{breadth (b)=2m}\end{cases}$

$\sf\implies Area\:of\:path=l\times b\\ \\ \sf\implies Area=120m\times 2m\\ \sf\implies Area=240m{}^{2}$

• The area of park which is parallel to breadth

$\begin{cases}\sf{Length (l)=2m}\\ \sf{breadth (b)=65m}\end{cases}$

$\sf\implies Area\:of\:path=l\times b\\ \\ \sf\implies Area=2m\times 65m\\ \sf\implies Area=130m{}^{2}$

Total Area of path

$\sf\implies 130m{}^{2}+240m{}^{2}\\ \sf\implies 370m{}^{2}$

• The area of middle portion of park
• It becomes a square of side 2m

$\boxed{\sf{Area\:of\:square=side{}^{2}}}$

$\sf middle\:part\:Area=2m\times 2m\\ \\ \sf\implies Middle\:part\:Area=4m{}^{2}$

• Now subtract the area of middle part of path from the total area of path

$\begin{cases}\sf{Total\:Area\:of\:path=370m{}^{2}}\\ \sf{Area\:of\:middle\:part=4m{}^{2}}\end{cases}$

$\sf Area\:of\:path =370m{}^{2}-4m{}^{2}\\ \\ \sf\implies Area\:of\:path=366m{}^{2}$

$\boxed{\sf{\purple{Area\:of\:path= 366m{}^{2}}}}$

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