Question

A PATH 5M WIDE RUN ALONG INSIDE A SQUARE PARK OF SIDE 100M. FIND THE AREA OF THE PATH. ALSO FIND THE COST OF CEMENTING IT AT RATE OF RS. 250 PER 10MSQUARE​

Answer 1

✬ Area = 1900 m² ✬

✬ Cost = Rs 47500 ✬

Step-by-step explanation:

Given:

• Width of path that is inside square park is 5 m.
• Measure of each side of square park is 100 m.
• Cost of cementing is Rs 250 per 10 m².

To Find:

• What is the area of the path & cost of cementing ?

Solution: Let ABCD be a square park. We have

• AB = BC = DC = AD = 100 m.

As we know that

★ Area of Square = Side² ★

➟ Area of ABCD = (100 × 100) m²

➟ 10000 m²

So the area of square park is 10000 m².

Now in square EFGH , we have

➙ EF = AB – ( 5 + 5 )

• EF = 100 – 10 = 90 m

➙ GF = BC – ( 5 + 5 )

• GF = 100 – 10 = 90 m

∴ Area of EFGH = Side²

➟ (90 × 90) m²

➟ 8100 m²

So the area of square EFGH is 8100 m².

• Area of path = Area (ABCD – EFGH)

$\implies{\rm }$ Ar. Path = (10000 – 8100)

$\implies{\rm }$ 1900 m²

Hence, the area of path is 1900 m².

• Cost of cementing per metre² = 250/10

• Rs 25 per m².

∴ Cost of cementing 1900 m² = 1900 × 25

➮ Rs 47500

Hence, cost of cementing path is Rs 47500.

Answer 2

Answer:

Given :-

• A path is 5 m wide run along inside a square park of side 100 m.

To Find :-

• What is the area of the path.
• What is the cost of cementing it at rate of Rs 250 per 10 m².

Solution :-

$\mapsto$ Let ABCD be the square park of side 100 m.

$\mapsto$ The path is 5 m wide.

Then,

$\implies$ PQ

$\implies$ 100 - (5 + 5)

$\implies$ 100 - 10

$\implies$ 90 m

Now, we have to find the area of square of ABCD :

As we know that,

$\longmapsto\sf\boxed{\bold{\pink{Area\: of\: Square =\: {(a)}^{2}}}}$

where,

• a = Side

Then, according to the question by using the formula we get,

$\implies \sf Area\: of\: Square =\: {(100)}^{2}$

$\implies \sf Area\: of\: Square =\: 100 \times 100$

$\implies \sf\bold{\green{Area\: of\: Square =\: 10000\: {m}^{2}}}$

Now, we have to find the area of the square PQRS :

$\implies \sf Area\: of\: Square =\: {(90)}^{2}$

$\implies \sf Area\: of\: Square =\: 90 \times 90$

$\implies \sf\bold{\green{Area\: of\: Square =\: 8100\: {m}^{2}}}$

Hence, the area of the path will be :

$\implies \sf Area\: of\: path =\: Area\: of\: ABCD - Area\: of\: PQRS$

$\implies \sf Area\: of\: path =\: 10000\: {m}^{2} - 8100\: {m}^{2}$

$\sf\bold{\red{Area\: of\: path =\: 1900\: {m}^{2}}}$

$\therefore$ The area of the path is 1900 m².

$\rule{150}{2}$

Now, we have to find the cost of cementing it at rate of Rs 250 per 10 m² :

If, cost of cementing for 10 m² is Rs 250.

Then, the cost of 1 m² is :

$\leadsto \sf \dfrac{25\cancel{0}}{1\cancel{0}}$

$\leadsto\sf{\purple{Rs\: 25}}$

Then, the cost of 1900 m² is :

$\leadsto \sf Cost\: of\: cementing\: path =\: 25 \times 1900$

$\leadsto \sf\bold{\red{Cost\: of\: cementing\: path =\: Rs\: 47500}}$

[Note : Please refer the attachment for the diagram. ]