Question:
The length of a ladder is exactly equal to the height of the wall it is leaning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then the height of the wall is
The length of a ladder is exactly equal to the height of the wall it is leaning against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then the height of the wall is
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When an object is raised on a platform, reduce the total vertical distance by platform height in Pythagoras.
Updated On: Aug 6, 2025
- 12 m
- 15 m
- 18 m
- 11 m
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The Correct Option is B
Solution and Explanation
Let height of wall = length of ladder = $h$.
From the stool top to the wall top: vertical height = $h - 3$, horizontal distance = 9 m.
Using Pythagoras:
\[
(h - 3)^2 + 9^2 = h^2
\]
\[
h^2 - 6h + 9 + 81 = h^2
\]
\[
-6h + 90 = 0 \Rightarrow h = 15 \ \text{m}.
\]
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