Question

A field is 90 m long and 70 m wide. It has two cross roads in its centre of
uniform width of 5 m, such that one road is parallel to its length and the
other is parallel to its breadth. Find the cost of gravelling the roads at Rs 3 per
square metre.​

Answer 1

Answer:

Rs. 2325

Step-by-step explanation:

Let ABCD be the rectangular field the EFGH and IJKL and the two rectangular roads with width 5 m

Given,

• that length of rectangular field = 90 m

• And breadth of rectangular field = 70 m

Area of rectangular field = length × breadth

➾ 90 m × 70 m

➾ 6300 m²

Area of the road EFGH = 70 m × 5 m

➾ 450 m²

Now, Area of road IJKL = 70 m × 5 m

➾ 350 m²

From the figure, it is clear that area of MNOP is common to the two road thus area of MNOP

➾ 5 m × 5 m

➾ 25 m²

Therefore,

Area of the road = Area of EFGH + Area of the road IJKL - Area of MNOP

➾ Area of road = ( 450 + 350) m² - 25 m²

➾ Area of road = 800 m² - 25 m²

➾ Area of road = 775 m²

Again, it is given that the cost of gravelling the road = Rs. 3 per m²

Therefore,

cost of gravelling 775 m² area of the roads

➾ Rs. ( 775 × 3)

➾ Rs. 2325

Hence, the cost of gravelling the roads is Rs. 2325 per square metre