Two cross roads each of width 5 m have been constructed in the middle of a garden crossing each other at right angles, running parallel to the sides of the garden 70 m long and45 m wide. Find the cost of constructing the roads at the rate of 80 per sq.m.
Question
Two cross roads each of width 5 m have been constructed in the middle of a garden crossing each other at right angles, running parallel to the sides of the garden 70 m long and45 m wide. Find the cost of constructing the roads at the rate of 80 per sq.m.
Solution
Sure, here is the step by step solution:
Step 1: Calculate the total area of the two roads.
The roads are crossing each other at right angles, so the area of the crossroads is a square of side 5m. The area of this square is 5m * 5m = 25 sq.m.
The total length of the roads is the sum of the length and the width of the garden, which is 70m + 45m = 115m. But we have already counted the crossroads twice (once for the length and once for the width), so we subtract the width of one road (5m) to avoid double counting. So the total length of the roads is 115m - 5m = 110m.
The width of the roads is 5m, so the total area of the roads is 110m * 5m = 550 sq.m.
Step 2: Add the area of the crossroads to the area of the roads.
The total area that needs to be constructed is 550 sq.m + 25 sq.m = 575 sq.m.
Step 3: Calculate the total cost of construction.
The cost of construction is 80 per sq.m, so the total cost is 575 sq.m * 80 = 46,000.
So, the cost of constructing the roads is 46,000.
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