Through a rectangular field of length 70 m and breadth 50 m, two roads are
constructed which are parallel to the sides and cut each other at right angles
through the centre of the fields. If the width of each road is 3 m, find (i) the area
covered by the roads. (ii) the cost of constructing the roads at of the rate of ₹ 130 per m
Answers
Given:
- Length of rectangular field = 70 m
- Breadth of rectangular field = 17 m
To find:
- Area of rectangular field?
- The cost of constructing the roads at of the rate of ₹ 130 per m.
Solution:
- Let's consider ABCD is a rectangle.
Where,
- Base = Length = 70 m
- Perpendicular = Breadth
- width = 3m
• Let Breadth of rectangle be b m.
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« By using area formula (l × b),
→ L × B = Area
→ 70 × 3 = 210
→ Area = 210m².
∴ Hence, Area of the road = 210m².
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« Finding area of road parallel to the breadth,
→ L × B = Area
→ 50 × 3 = 150
→ Area = 150m².
∴ Hence, Area of the road parallel to breadth = 150m².
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« Now, Let's find area of two roads.
→ 210m² + 150m² - 9m²
→ 360m² - 9m²
→ 351m²
∴ Hence, Area of two roads is 351m²
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« Lastly let's find cost of constructing the roads.
→ 130 × 351
→ 45630 rupees.
∴ Hence, Cost of constructing the roads is 45630 rupees.
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Therefore, The area covered by roads is 351m² & The cost of constructing the roads at of the rate of ₹ 130 per m is 45630 rupees.