Question

7. An artificial rectangular pond measuring 50 m by 40 m hos two paths each of width 5 m crossing
each other at right angles. Each path is parallel to one of the sides. Find the area of the path.​

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Length\:of \: Pond\: ( l ) = 50 m} \\ \sf{Breadth \: of \: Pond \: ( b ) = 40 m}\\ \sf{Width \: of \: the \: Road \:( w ) = 5 m} \\\sf{Area \:of \:Road = ?}\end{cases}$

⋆ Refrence of Image is in the Attachment :

• According to the Question Now :

$\implies \tt Area \:of \:Road = (Area \: of \:Park) - (Area \: of \: \\\qquad \qquad \qquad \qquad \:\: \:\tt Parts \:Excluding \: the \: Road) \\ \\\implies \tt Area\:of \:Road = ( l b ) - [(l - 2)(b - 2)] \\ \\\implies \tt Area \: of \: Road = (50 \times 40) - [(50 - 5) \times(40 - 5)] \\ \\\implies \tt Area \: of \:Road = 2000 - ( 45 \times 35) \\ \\\implies \tt Area \:of \: Road = 2000 - 1575 \\ \\\implies \boxed{\red{\tt Area \:of \:Road = 425 \:{m}^{2}}}$

⠀

∴ Therefore, Area of the Road is 425 m²

$\rule{300}{2}$

• S H O R T C U T ⠀T R I C K :

$\longrightarrow \tt Area \:of \:Road = [(Length + Breadth) - Width] \times Width \\ \\\longrightarrow \tt Area \:of \:Road = [(50 + 40) - 5] \times5 \\ \\\longrightarrow \tt Area \:of \:Road = [90 - 5] \times 5 \\ \\\longrightarrow \tt Area \:of \:Road = 85 \times 5 \\ \\\longrightarrow \boxed{\red{\tt Area \:of \:Road = 425 \: {m}^{2}}}$

⠀

∴ Therefore, Area of the Road is 425 m²

Answer 2

❏ Formula Used:-

for a rectangle of length l and breadth b ,

(1) Area is given by the formula,

$\sf\longrightarrow \boxed{Area=(length\times breadth)}$

(2) Perimeter is given by the Formula,

$\sf\longrightarrow \boxed{Perimeter=2\times(length+ breadth)}$

❏ Solution:-

Q)

An artificial rectangular pond measuring 50 m by 40 m hos two paths each of width 5 m crossing

each other at right angles. Each path is parallel to one of the sides. Find the area of the path.

Ans)(plz, Refer to the fig. attached above)

☞for the rectangular pond

• length(l)=50 m
• breadth (b)=40 m
• Area=(50×40)m²=2,000 m²

☞For each small rectangular portion

• length=$\sf(\frac{50-5}{2} )=22.5 \:m$
• breadth=$\sf(\frac{40-5}{2} )=17.5 \:m$
• Area=(22.5×17.5)m²=393.75 m²

$\because \sf All\: these \:four\: rectangular\: portions \\ \:are \:of \:same \:size , so \:each\: rectangular\: \\ portion\: would\: have\: the \:same \:area =393.75\:m{}^{2}$

$\therefore \sf Area\: of \:all\: 4\: rectangular\: portions\:=(4\times393.75)\:m{}^{2}$

$\longrightarrow \sf Area\: of \:all\: 4\: rectangular\: portions\:=1575\:m{}^{2}$

∴Area of the path=(2000-1575)m²=425 m²

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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