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A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street?
  • a)
    21 m
  • b)
    20 m
  • c)
    12 m
  • d)
    15 m
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A ladder 15 m long reaches a window which is 9 m above the ground on o...

In ΔABE,
AE2 + AB2 = BE2
⇒ 92 + AB2 = 152
⇒ AB2 = 225 - 81
= 144
⇒ AB = 12 m
Similarly,
In DBCD
⇒ BC2 = BD2 - DC2 = 152 - 122 = 92
BC = 9m
∴ width of street = (AB + BC) = 12 + 9 = 21 m
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A ladder 15 m long reaches a window which is 9 m above the ground on o...
Understanding the Problem
To find the width of the street, we can use the Pythagorean theorem. The ladder acts as the hypotenuse of two right triangles formed on either side of the street.
Given Data
- Length of the ladder (hypotenuse) = 15 m
- Height of the first window = 9 m
- Height of the second window = 12 m
Calculating Width of the Street
1. First Triangle (Ladder to First Window)
- Let the width of the street be 'w'.
- Using the Pythagorean theorem:
  • \( (15)^2 = (9)^2 + w^2 \)
  • \( 225 = 81 + w^2 \)
  • \( w^2 = 225 - 81 \)
  • \( w^2 = 144 \)
  • \( w = \sqrt{144} = 12 \, m \)


2. Second Triangle (Ladder to Second Window)
- The height is 12 m (same width 'w'):
  • \( (15)^2 = (12)^2 + w^2 \)
  • \( 225 = 144 + w^2 \)
  • \( w^2 = 225 - 144 \)
  • \( w^2 = 81 \)
  • \( w = \sqrt{81} = 9 \, m \)


Finding the Total Width
- Since the calculated width for each triangle differs, we add both widths to find the total width of the street:
Total Width = Width to First Window + Width to Second Window
- \( Total Width = 12 m + 9 m = 21 m \)
Conclusion
The width of the street is 21 m, confirming that the correct answer is option 'A'.
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A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street?a)21 mb)20 mc)12 md)15 mCorrect answer is option 'A'. Can you explain this answer?
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