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 to calculate the total length of the roads in a park that are to be covered with stones. It provides the dimensions of the park and the width of the roads, implying that we need to consider both the horizontal and vertical road lengths, subtracting any overlaps.
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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Calculate the dimensions of the park The park is 20 m long and 15 m wide.
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Determine the layout of the roads Each road is 2 m wide. There are one horizontal road and one vertical road crossing each other.
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Calculate the length of the horizontal road The length of the horizontal road is equal to the length of the park: $$ \text{Length of horizontal road} = 20 , \text{m} $$
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Calculate the length of the vertical road The length of the vertical road is equal to the width of the park: $$ \text{Length of vertical road} = 15 , \text{m} $$
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Account for the overlap at the intersection Since the roads overlap where they cross, we must subtract the width of the overlap. The width is 2 m (the width of one road): $$ \text{Overlap} = 2 , \text{m} $$
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Calculate the total length to be paved by stones Total length is the sum of the lengths of the roads minus the overlap: $$ \text{Total length} = (\text{Length of horizontal road} + \text{Length of vertical road} - \text{Overlap}) $$ Substituting values: $$ \text{Total length} = (20 + 15 - 2) , \text{m} $$
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Calculate the final answer Performing the calculation: $$ \text{Total length} = 20 + 15 - 2 = 33 , \text{m} $$
The total length to be paved by stones is $33 , \text{m}$.
More Information
In this problem, you have combined the lengths of two roads and subtracted the overlapping section to find the total length that needs to be covered. This method ensures that each segment is counted only once.
Tips
- Not subtracting the overlap: It’s crucial to remember that when two roads intersect, you must account for the overlapping length to avoid double-counting.
- Confusing road lengths: Ensure to use the correct dimensions for horizontal and vertical roads in the calculations.
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