Question

A rectangular field is 30 m in lengthand 22 m in width two mutually perpendicular roads each 2.5 m wide are drawn inside the field so that one road is parallel to the length of the field and the other road is parallel to its width calculate the area of the crossroads

Answer 1

$\huge\mathbb{\purple{SOLUTION:-}}$

$\bold{Dimensions}\begin{cases}\sf{length (l)=30m}\\ \sf{Breadth (b)=22m}\end{cases}$

$\bf\underline{\underline{According\:to\: Question:-}}$

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

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

$\bf{we\:have}\begin{cases}\sf{Length (l)=30m}\\ \sf{breadth (b)=2.5m}\end{cases}$

$\sf\implies Area=l\times b\\ \\ \sf\implies Area=30m\times 2.5m\\ \sf\implies Area=75m{}^{2}$

• The area of park which is parallel to breadth

$\begin{cases}\sf{Length (l)=2.5m}\\ \sf{breadth (b)=22m}\end{cases}$

$\sf\implies Area=l\times b\\ \\ \sf\implies Area=2.5m\times 22m\\ \sf\implies Area=55m{}^{2}$

• Area of middle part of path which Cross the path two times it becomes square of side 2.5m

$\boxed{\sf{Area\:of\:square=side\times side}}\\ \\ \sf\implies Area=2.5m\times 2.5m\\ \\ \sf\implies Area=6.25m{}^{2}$

• Total Area of path

$\sf\implies Total\:Area\:of\:park=75+55-6.25\\ \sf\implies 130m{}^{2}-6.25m{}^{2}\\ \sf\implies Area=123.75m{}^{2}$

$\boxed{\sf{Area\:of\:path=123.75m{}^{2}}}$

#BAL

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