Question:
A plot of land 45m* 65m is divided into four equal rectangular plots by 2 roads that are perpendicular to each other. If the width of the roads is 5 m, find the area of the crossroads.
A plot of land 45m* 65m is divided into four equal rectangular plots by 2 roads that are perpendicular to each other. If the width of the roads is 5 m, find the area of the crossroads.
Updated On: Jan 13, 2026
- 625 sq.m.
- 525 sq.m.
- 550 sq.m.
- 600 sq.m.
- 652 sq.m
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The Correct Option is B
Solution and Explanation
Step 1: Understand the problem.
A plot of land has dimensions 45 meters by 65 meters. It is divided into four equal rectangular plots by two roads that are perpendicular to each other. The width of each road is 5 meters. We are asked to find the area of the crossroads, where the two roads intersect.
Step 2: Calculate the total area of the plot.
The total area of the plot is given by the formula:
Total area = Length × Width = \( 45 \times 65 = 2925 \, \text{sq.m.} \)
Step 3: Calculate the area of the roads.
The roads divide the plot into four equal parts. Since the roads are perpendicular to each other, we need to calculate the area occupied by both roads.
- The horizontal road divides the plot into two parts, and its width is 5 meters. Therefore, the area of the horizontal road is:
Area of horizontal road = Length × Width of the road = \( 45 \times 5 = 225 \, \text{sq.m.} \)
- The vertical road divides the plot into two parts, and its width is also 5 meters. Therefore, the area of the vertical road is:
Area of vertical road = Width × Width of the road = \( 65 \times 5 = 325 \, \text{sq.m.} \)
Step 4: Calculate the area of the crossroads.
The area of the crossroads is the overlap of the two roads. Since both roads have a width of 5 meters, the area of the intersection is a square of side 5 meters:
Area of crossroads = \( 5 \times 5 = 25 \, \text{sq.m.} \)
Step 5: Calculate the total area of the roads.
The total area occupied by the two roads is:
Total area of roads = Area of horizontal road + Area of vertical road - Area of crossroads (since the crossroads are counted twice)
Total area of roads = \( 225 + 325 - 25 = 525 \, \text{sq.m.} \)
Step 6: Conclusion.
The area of the crossroads is 525 sq.m.
Final Answer:
The correct option is (B): 525 sq.m.
A plot of land has dimensions 45 meters by 65 meters. It is divided into four equal rectangular plots by two roads that are perpendicular to each other. The width of each road is 5 meters. We are asked to find the area of the crossroads, where the two roads intersect.
Step 2: Calculate the total area of the plot.
The total area of the plot is given by the formula:
Total area = Length × Width = \( 45 \times 65 = 2925 \, \text{sq.m.} \)
Step 3: Calculate the area of the roads.
The roads divide the plot into four equal parts. Since the roads are perpendicular to each other, we need to calculate the area occupied by both roads.
- The horizontal road divides the plot into two parts, and its width is 5 meters. Therefore, the area of the horizontal road is:
Area of horizontal road = Length × Width of the road = \( 45 \times 5 = 225 \, \text{sq.m.} \)
- The vertical road divides the plot into two parts, and its width is also 5 meters. Therefore, the area of the vertical road is:
Area of vertical road = Width × Width of the road = \( 65 \times 5 = 325 \, \text{sq.m.} \)
Step 4: Calculate the area of the crossroads.
The area of the crossroads is the overlap of the two roads. Since both roads have a width of 5 meters, the area of the intersection is a square of side 5 meters:
Area of crossroads = \( 5 \times 5 = 25 \, \text{sq.m.} \)
Step 5: Calculate the total area of the roads.
The total area occupied by the two roads is:
Total area of roads = Area of horizontal road + Area of vertical road - Area of crossroads (since the crossroads are counted twice)
Total area of roads = \( 225 + 325 - 25 = 525 \, \text{sq.m.} \)
Step 6: Conclusion.
The area of the crossroads is 525 sq.m.
Final Answer:
The correct option is (B): 525 sq.m.
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