CBSE 2025, Set 1

Question

**Case Study - 2**
A ladder of fixed length 'h' is to be placed along the wall such that it is free to move along the height of the wall.
![Diagram Ladder](https://www.edvaya.com/images/cbse/mathematics/2025/set1/q37-ladder.webp)

Based upon the above information, answer the following question:
(i) Express the distance ($y$) between the wall and foot of the ladder in terms of '$h$' and height ($x$) on the wall at a certain instant. Also, write an expression in terms of $h$ and $x$ for the area ($A$) of the right triangle, as seen from the side by an observer.

Edvaya · Accepted Answer

The correct answer is Subjective. Let the height on the wall be $x$, the distance from the foot of the ladder to the wall be $y$, and the length of the ladder be $h$. The wall, the ground, and the ladder form a right-angled triangle. Using Pythagoras theorem: $x^2 + y^2 = h^2$ $y^2 = h^2 - x^2$ $y = \sqrt{h^2 - x^2}$ (Taking the positive root since distance cannot be negative) The area of a right-angled triangle is $A = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$. $A = \frac{1}{2}yx$ Substituting the expression for $y$: $A = \frac{1}{2}x\sqrt{h^2 - x^2}$

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Mathematics > Calculus > Application Of Derivatives

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