Question

A SQUARE GRASS PLOT 600 METRES LONG IS BODRED ON THE OUTSIDE BY A PATH 10 METRE WIDE.Find the cost of paying the path at ₹250 per 100m.​

Answer 1

Answer:

RS. 52500

Step-by-step explanation:

Given inner side of square park, s=100 cm

Area of inner square =100

2

=10000 cm

2

width of path,w=5 cm

Outer side of square =100+5+5=110 cm

Area of outer square =110

2

=12100 cm

2

Area of path =12100−10000=2100 cm

2

Cost of cementing at the rate of Rs 250 per 10 sq cm = Rs 250×210= Rs 52500

∴ Cost of cementing a 2100 cm

2

path =Rs. 52500

Answer 2

$\large\underline{\sf{Given- }}$

A square grassy plot of length 600 m.

Bordered by a outside path of width 10 m.

Cost of paying the path is ₹ 250 per 100 square m.

$\large\underline{\sf{To\:Find - }}$

The Cost of paying the path

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\red{\boxed{ \bf{ \: Area_{(square)} = {side}^{2} }}}$

$\large\underline{\sf{Solution-}}$

Dimensions of inner square ABCD

Side of inner square, AB = 600 m

So,

Area of inner square ABCD is

$\rm :\longmapsto\:Area_{(square \: ABCD)} = {side}^{2}$

$\rm :\longmapsto\:Area_{(square \: ABCD)} = {600}^{2}$

$\bf :\longmapsto\:Area_{(square \: ABCD)} = 360000 \: {m}^{2}$

Dimensions of outer square PQRS

Length of inner square = 600 m

Width of path = 10 m

So,

Length of outer square = Length of inner square + width

Thus,

Length of outer square, PQ = 600 + 10 = 610 m

So,

Area of outer square, PQRS is

$\rm :\longmapsto\:Area_{(square \: PQRS)} = {side}^{2}$

$\rm :\longmapsto\:Area_{(square \: PQRS)} = {610}^{2}$

$\bf :\longmapsto\:Area_{(square \: PQRS)} = 372100 \: {m}^{2}$

Now,

Area of path = Area of outer square PQRS - Area of inner square ABCD

So,

$\rm :\longmapsto\:Area_{(path)} = Area_{(square \: PQRS)} - Area_{(square \: ABCD)}$

$\rm \: = \: \:372100 - 360000$

$\rm \: = \: \:12100 \: {m}^{2}$

$\bf\implies \:Area_{(path)} = 12100 \: {m}^{2}$

Now,

According to statement,

Cost of paying 100 m² is ₹ 250

Cost of paying 12100 m² is

$\rm \: = \: \:\dfrac{250}{100} \times 12100$

$\rm \: = \: \:250 \times 121$

$\rm \: = \: \:30250$

So, Cost of paying 12100 m² is ₹ 30250.

Additional Information

$\red{\boxed{ \bf{ \: Area_{(rectangle)} = length \times breadth}}}$

$\red{\boxed{ \bf{ \: Area_{(rhombus)} = base \times height}}}$

$\red{\boxed{ \bf{ \: Area_{(parallelogram)} = base \times height}}}$

$\red{\boxed{ \bf{ \: Area_{(circle)} = {\pi \: r}^{2} }}}$