A park 20 m long and 15 m broad has 2 m wide roads crossing each other as shown. The sides of the roads which have been covered with stones are shown by dotted lines. Find the tota... A park 20 m long and 15 m broad has 2 m wide roads crossing each other as shown. The sides of the roads which have been covered with stones are shown by dotted lines. Find the total length to be paved by stones.
Understand the Problem
The question is asking for the total length of roads in a park that are covered with stones, given the dimensions of the park and the width of the roads. This involves calculating the lengths of the intersecting roads and considering their overlap.
Answer
The total length to be paved by stones is \( 33 \, \text{m} \).
Answer for screen readers
The total length to be paved by stones is ( 33 , \text{m} ).
Steps to Solve
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Identify the Dimensions and Road Width The park dimensions are given as length = 20 m and width = 15 m. The width of each road is 2 m.
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Calculate the Length of the Horizontal Road The horizontal road will span the length of the park. Since it's 2 m wide, the length of the stone coverage for the horizontal road is: $$ L_{\text{horizontal}} = 20 , \text{m} $$
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Calculate the Length of the Vertical Road The vertical road will span the width of the park. Similarly, the length of the stone coverage for the vertical road is: $$ L_{\text{vertical}} = 15 , \text{m} $$
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Calculate the Overlap of Roads Since the roads intersect, we need to subtract the overlap area. The width at which the two roads intersect (which is also the width of either road) is 2 m.
The length of the overlapping area is 2 m and the width is the width of one road (which is also 2 m): $$ L_{\text{overlap}} = 2 , \text{m} $$
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Total Length of the Roads Paved with Stones Finally, we compute the total length of the roads to be paved by stones by adding the lengths of both roads and subtracting the overlap: $$ L_{\text{total}} = L_{\text{horizontal}} + L_{\text{vertical}} - L_{\text{overlap}} $$ $$ L_{\text{total}} = 20 , \text{m} + 15 , \text{m} - 2 , \text{m} $$
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Final Calculation Perform the final addition and subtraction to find the total length paved: $$ L_{\text{total}} = 20 + 15 - 2 = 33 , \text{m} $$
The total length to be paved by stones is ( 33 , \text{m} ).
More Information
This calculation assumes that the roads are rectangular, intersecting at right angles, and the overlap area is accounted for to avoid double counting.
Tips
- Failing to account for the overlap between the two roads, leading to an overestimation of the total length.
- Miscalculating the dimensions of the roads, particularly forgetting the width when determining areas.
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