Question

ise 15.4
A rectangular plot 200 m * 150 m has
three 3 m wide roads along the length
of the plot on either side and one in the
middle. On either side of the middle
road, there are shops.
a) Find the area covered by the shops.
b) Also, find the cost of reconstructing
the roads at the rate of 225 per m​

Answer 1

Understanding the Question:

This question says that a rectangular plot having dimensions 200 m into 150 m has three 3 m wide roads along the length of the plot on either side and one in the middle. On either side of the middle road, there are shops. The following we have to find: 1) The area covered by the shops. 2) The cost of reconstructing the roads at the rate of 225 per metres.

Given that:

• Length of rectangular plot = 200 metres.

• Breadth of rectangular plot = 150 metres.

• The rectangular plot is surrounded with three roads.

• The roads are 3 metres in breadth.

• Roads along the length of the plot on either side and one in the middle.

• On either side of the middle road, there are shops.

To find:

• The area covered by the shops.

• The cost of reconstructing the roads at the rate of 225 per metres.

Solution:

• The area covered by the shops = 28200 m sq.
• The cost of reconstructing the roads at the rate of 225 per metres = Rupees 4,05,000

Using formulas:

• Formula to find out the area of the rectangle means the area of the rectangular plot = Length × Breadth.

• Formula to find the area of three roads = 3 × Length of the rectangular plot × Breadth of the road.

• Formula to find out the area covered by the shops = Area covered by the plot - Area covered by three roads.

• Formula to find out the cost of reconstructing the roads at the rate of 225 per metres = 225 × Area covered by three roads.

Full Solution:

• Firstly let us find the area of rectangular plot by using the above mentioned formula.

→ Length of rectangular plot = 200 metres.

→ Breadth of rectangular plot = 150 metres.

→ Area of rectangle = Length × Breadth

→ Area of rectangular plot = Length × Breadth

→ Area of rectangular plot = (200×150) metres

→ Area of rectangular plot = 30,000 metres sq.

• Now let us find the the area of three roads by using the above mentioned formula.

→ The area of three roads = 3 × Length of the rectangular plot × Breadth of the road

→ The area of three roads = 3 × 200 × 3

→ The area of three roads = 9 × 200

→ The area of three roads = 1800 metres sq.

• Now let us find the area covered by the shops by using the above mentioned formula.

→ The area covered by the shops = Area covered by the plot - Area covered by three roads.

→ The area covered by the shops = 30,000 - 1,800

→ The area covered by the shops = 28,200 metres sq.

• Now at last let us find the cost of reconstructing the roads at the rate of 225 per metres by using the above mentioned formula.

→ 225 × Area covered by three roads.

→ 225 × 1800

→ Cost = Rupees 4,05,000

Answer 2

Answer:

$\large{\underline{\sf{\pmb{{\maltese{Given}}}}}}$

• Length and breadth of rectangular plot is 200 cm and 150 cm.
• Three 3 m wide roads along the length of the rectangular plot.
• Roads along the length of the plot on either side and one in the middle.
• On either side of the middle road, there are shops.

$\large{\underline{\sf{\pmb{{\maltese{To \: Find }}}}}}$

• Area covered by the shops.
• The cost of reconstructing the roads at the rate of 225 per m

$\large{\underline{\sf{\pmb{{\maltese{Using \: Formulae}}}}}}$

$\circ\underline {\boxed {\sf{Area \: of \: Rectangle = Lenght \times Breadth }}}$

$\circ\underline {\boxed {\sf{Area \: of \: rectangular \: 3 \: roads=3 \times Length \: of \: rectangular \: plot\times 3 \: m \: road }}}$

$\circ \underline { \boxed{\sf{Area \: covered \: by \: shop = Area \: of \: rectangular \: plot - Area \: of \: covered \: by \: 3 \: roads}}}$

$\circ \underline{\boxed{ \sf{Cost \: of \: reconstructing \: roads = rate \: of \: per \: meter \times Area \: covered \: by \: three \: roads }}}$

$\large{\underline{\sf{\pmb{{\maltese{Solution}}}}}}$

$\bigstar \: \underline\frak{Firstly,finding \: the \: area \: of \: rectangular \: plot }$

${\implies {\sf{Area \: of \: rectangular \: plot = Lenght \times Breadth }}}$

• Substituting the values

${\implies {\sf{Area \: of \: Rectangular \: plot = 200 \times 150 }}}$

${\implies {\sf{Area \: of \: Rectangular \: plot = 30000 \: {cm}^{2} }}}$

$\star\underline{\boxed{\sf \pink{Area \: of \: Rectangular \: plot = 30000 \: {m}^{2} }}}$

$\bigstar \: \underline \frak{Now,finding \: the \: area \: of \: three \: roads}$

${ \implies{\sf{Area \: of \: rectangular \: 3 \: roads = 3 \times Length \: of \: rectangular \: plot\times 3 \: m \: road}}}$

• Substituting the values

${ \implies{\sf{Area \: of \: rectangular \: 3 \: roads = 3 \times200 \: m\times 3 \: m }}}$

${ \implies{\sf{Area \: of \: rectangular \: 3 \: roads = 600 \: m\times 3 \: m }}}$

${ \implies{\sf{Area \: of \: rectangular \: 3 \: roads =1800 \: {cm}^{2} }}}$

$\star \underline{\boxed{\sf \pink{Area \: of \: rectangular \: 3 \: roads =1800 \: {m}^{2} }}}$

$\bigstar \underline\frak{Now,finding \: area \: covered \: by \: shop}$

${ \implies{\sf{Area \: covered \: by \: shop = Area \: of \: rectangular \: plot - Area \: of \: covered \: by \: 3 \: roads}}}$

• Substituting the values

${ \implies{\sf{Area \: covered \: by \: shop =30000 \: {cm}^{2} - 1800 \: {cm}^{2} }}}$

${ \implies{\sf{Area \: covered \: by \: shop = 28200 \: {m}^{2} }}}$

$\star \underline{ \boxed{\sf \pink{Area \: covered \: by \: shop = 28200 \: {m}^{2} }}}$

$\bigstar \: \underline \frak{Now,finding \: the \: total \: cost \: of \: reconstructing \: the \: roads \: at \: the \: rate \: of \: 225 \: {m}^{2} }$

${\implies\sf{Cost \: of \: reconstructing \: roads = rate \: of \: per \: meter \times Area \: covered \: by \: three \: roads }}$

• Substituting the values

${\implies{ \sf{Cost \: of \: reconstructing \: roads = 225\times 28200 }}}$

${\implies{ \sf{Cost \: of \: reconstructing \: roads =Rs.405000 }}}$

$\star\underline {\boxed{ \sf \pink{Cost \: of \: reconstructing \: roads =Rs.405000 }}}$

• Henceforth,The area covered by the shops is 28200 m² and the cost of reconstructing the roads is 405000 rupees.