Question

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16. A rectangular lawn 75 m by 60 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at 14.50 per sq. metre.

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Answer 1

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Length of the rectangular lawn=75m

Breadth of the lawn=60m

Width of the road=4m

Area of the road (ABCD) parallel to the length of the lawn

→ 75m×4m → 300m

Area of the road(EFGH) parallel to the breadth of the lawn

→ 60m×4m → 240m

Area of the common area in both ABCD and EFGH

→ 4m×4m → 16m

Total area of both the rectangular roads

→ 300+240−16

→ 524m

Cost of gravelling the roads per m

→ Rs.14.50

Cost of gravelling the roads for 524m

→ 14.50×524

→ 7,598 Rupees

Cost of gravelling the road is Rs.7598 .

Answer 2

ANSWER:

Given:

• Length of lawn = 75m
• Breadth of lawn = 60m
• Width of roads running in it = 4m

To Find:

• Cost of gravelling the roads @ Rs14.50per sq. metre

Solution:

(Refer the attachment for diagram)

ABCD is the lawn. In which,. PQRS and WXYZ are the roads. The small box EFGH is the part where the two roads intersect.

So,

⇒ Dimensions of the road PQRS = 75m by 4m

⇒ Dimensions of the road WXYZ = 60m by 4m

Now,

⇒ Area the road PQRS = 75m * 4m

⇒ Area of the road PQRS = 300m² ------(1)

And,

⇒ Area of the road WXYZ = 60m * 4m

⇒ Area of the road WXYZ = 240m² ------(2)

Finally,

⇒ Dimensions of the common part EFGH = 4m by 4m

⇒ Area of the common part EFGH = 4m * 4m

⇒ Area of the common part EFGH = 16m² ------(3)

Therefore,

⇒ Total Area of the roads = (Area of PQRS) + (Area of WXYZ) - (Area of EFGH)

This is because area of that part is being counted in the areas of both roads. So, we need to subtract it once.

From (1), (2) & (3),

⇒ Total Area of the roads = 300m² + 240m² - 16m²

⇒ Total Area of the roads = 540m² - 16m²

⇒ Total Area of the roads = 524m² ------(4)

Hence,

⇒ Cost of gravelling the roads per sq. metre = Rs 14.50

Therefore,

⇒ Cost of gravelling 524m² of road = Rs(14.50 * 524)

⇒ Cost of gravelling 524m² of road = Rs7598

So, the cost of gravelling the roads is Rs 7598.

Formula Used:

• Area of rectangle = length * breadth