Question

A rectangular lawn, 75m by 60m, has two roads, each road 4m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at ₹50 per m².​

Answer 1

Question :

A rectangular lawn, 75m by 60m, has two roads, each road 4m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at ₹50 per m².

Solution :

★ Finding area of road ABCD :

ㅤㅤㅤ→ㅤAr(ABCD) = L × B

★ Values that we have :

• L = 75 m
• B = 4 m

★ Putting all values :

ㅤㅤㅤ→ㅤAr(ABCD) = 75 × 4

ㅤㅤㅤ→ㅤAr(ABCD) = 300 m²

★ Finding area of road PQRS :

ㅤㅤㅤ→ㅤAr(PQRS) = L × B

★ Values that we have :

• L = 60 m
• B = 4 m

★ Putting all values :

ㅤㅤㅤ→ㅤAr(PQRS) = 60 × 4

ㅤㅤㅤ→ㅤAr(PQRS) = 240 m²

★ Finding common area b/w roads [Ar(EFGH)] :

ㅤㅤㅤ→ㅤAr(EFGH) = Side²

★ Values that we have :

• Side = 4 m

★ Putting all values :

ㅤㅤㅤ→ㅤAr(EFGH) = (4)²

ㅤㅤㅤ→ㅤAr(EFGH) = 16 m²

★ Total area of roads :

ㅤㅤㅤ→ㅤ(300 + 240) - 16

ㅤㅤㅤ→ㅤ540 - 16

ㅤㅤㅤ→ㅤ524 m²

∴Total area of roads = 524 m²

★ Cost of gravelling the roads :

ㅤㅤㅤ→ㅤ₹(524 × 50)

ㅤㅤㅤ→ㅤ₹ 26,200

∴Cost of gravelling the roads = ₹ 26,200

★ Formulae used above :

• Area of rectangle = L × B
• Area of square = Side²

★ Note :

• Diagram is in the attachment !

━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

*Question:-

A rectangular lawn, 75m by 60m, has two roads, each road 4m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at ₹50 per m².

*Answer

₹26200....

Step-by-step explanation:

We know that for the road ABCD

It is given that,

• length = 75m
• breadth = 4m

We know that,

Area of road ABCD =l×b

By substituting the values,

Area of road ABCD = 75×4

So we get,

Area of road ABCD = 300m²

We know that for the road PQRS

It is given that,

• length = 60m
• breadth = 4m

We know that,

Area of road PQRS =l×b

By substituting the values,

Area of road PQRS = 60×4

So we get,

Area of road PQRS = 240m²

We know that for road EFGH

It is given that,

• Side = 4m
• Area of road EFGH = side²

By substituting the value,

Area of road EFGH =4² = 16m²

The total area of the road for gravelling

• = Area of road ABCD + Area of road PQRS - Area of road EFGH.

By substituting the values,

Total area of the road for gravelling

• = 300 + 340 – 16

So we get,

Total area of the road for gravelling = 524m²

It is given that the cost of gravelling the road=₹50 per(m)²

So the cost of gravelling = 524m²

Road = ₹(50×524) = ₹26200

Therefore, the cost of gravelling the road is ₹26200.

$hope \: it \: helps$