Question

14) Through the rectangular field of length 70m and breadth 45m ,two cross
roads are constructed which is parallel to the sides and cut each other at
right angles through the centre of the field. If the width of each road is
5m,find the area covered by the roads, and the cost of constructing the
roads at the rate of 105 per sq.m.​

Answer 1

Question :-

Through the rectangular field of length 70m and breadth 45m ,two cross roads are constructed which is parallel to the sides and cut each other at right angles through the centre of the field. If the width of each road is 5m,find the area covered by the roads, and the cost of constructing the roads at the rate of 105 per sq.m.

Required Answer:-

Given:-

$\sf{ \rightarrow{Length \: of \: the \: rectangular \: field \: is \: 70m}}$

$\sf{ \rightarrow{Breadth \: of \: the \: rectangular \: field \: is \: 45m}}$

$\sf{ \rightarrow{Width \: of \: the \: each \: road \: is \: 5m}}$

To Find:-

$\sf{ \rightarrow{Area \: covered \: by \: the \: roads}}$

$\sf{ \rightarrow{The \: cost \: of \: constructing \: the \: roads}}$

♡ Solution:-

As we know that:-

$\underline{ \boxed{ \rm{ \blue{Area \: of \: a \: rectangle = length \times breadth}}}}$

First, let's find the area of the roads.

Note that:-

• Length of the first road = 70m
• Breadth of the first road = 5m

Hence,

$\sf{area \: of \: the \: first \: road = 70m \times 5m}$

$\\ \sf{ \implies{{Area \: of \: the \: first \: road = (70 \times 5)sq.m.}}}$

$\\ \sf{ \implies{Area \: of \: the \: first \: road = \bold{350sq.m.}}}$

Now, let's find the area of the second road.

• Length of the first road = 45m
• Breadth of the first road = 5m

$\sf{Area \: of \: the \: second\: road = 45m \times 5m}$

$\\ \sf{ \implies{{Area \: of \: the \: second \: road = (45 \times 5)sq.m.}}}$

$\\ \sf{ \implies{Area \: of \: the \: second \: road = \bold{225sq.m.}}}$

Now, we have to find the area of the common part where the roads crossed.

$\sf{Area \: of \: the \: common = 5m \times 5m}$

$\\ \sf{ \implies{{Area \: of \: the \: common \: part= (5 \times 5)sq.m.}}}$

$\\ \sf{ \implies{Area \: of \: the \: comon \: part = \bold{25sq.m.}}}$

Therefore:-

$\sf{Area \: of \: the \: roads =( 350 + 225 - 25)sq.m.}$

$\\ \sf{ \implies{Area \: of \: the \: roads = \orange{550sq.m.}}}$

Therefore area of the roads = 550sq.m.

Again,

$\sf{Cost \: of \: constructing \: th \: roads =Rs. (105 \times 550)}$

$\\ \sf{ \implies{Cost \: of \: constructing \: th \: roads =Rs. \orange{57750}}}$

Therefore, cost of constructing the roads is Rs. 57750

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Note:- For more explanation kindly see the attachment.