Question:

Perimeter $2r + 2y + \pi r = 10 \Rightarrow y = 5 - \left(1 + \dfrac{\pi}{2}\right)r$. [1.0 Mark]
Area $A(r) = 10r - \left(2 + \dfrac{\pi}{2}\right)r^2 \Rightarrow \dfrac{dA}{dr} = 10 - (4+\pi)r = 0$. [2.0 Marks]
Radius $r = \dfrac{10}{\pi + 4}\text{ m}$. Verify $\dfrac{d^2 A}{dr^2} < 0$. [0.5 Mark]
Dimensions: Length $= \dfrac{20}{\pi+4}\text{ m}$, Height $= \dfrac{10}{\pi+4}\text{ m}$. [1.5 Marks]

---
🎯 Official CBSE Marking Scheme:
Setting up perimeter constraint and height $y$: 1.0 Mark
Formulating area function and solving $r = 10/(\pi+4)$: 2.0 Marks
Applying Second Derivative Test: 0.5 Mark
Evaluating dimensions of window: 1.5 Marks