A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…
Mathematics20228 marksCase based
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window as shown in the figure given below. The total perimeter of the window is 10 m.
Based on the above information answer the following by choosing the correct option:
(i)[2.0]
If the length and breadth of the rectangle portion of the window is $y$ and $x$ respectively (as shown in the figure above) then the relation between the variable is
(a)$y = \frac{20 + (\pi - 2)x}{4}$
(b)$y = \frac{20 - (\pi + 2)x}{2}$
(c)$y = \frac{20 - (\pi + 4)x}{4}$
(d)$y = \frac{20 - (\pi + 2)x}{4}$
(ii)[2.0]
Let A be the area of the Norman window which admits the sunlight. Then A expressed in terms of $x$ is
(a)$A = 5x + \frac{\pi}{4}x^2 - 2x^2$
(b)$A = 5x + \frac{\pi}{8}x^2 - \frac{1}{2}x^2$
(c)$A = 5x - \frac{\pi}{8}x^2 - \frac{1}{2}x^2$
(d)$A = 5x - \frac{\pi}{2}x^2 - \frac{1}{4}x^2$
(iii)[2.0]
For the maximum value of A what will be the radius of the semicircle?
(a)$\frac{10}{2+\pi}$
(b)$\frac{10}{\pi-2}$
(c)$\frac{10}{4+\pi}$
(d)$\frac{20}{4-\pi}$
(iv)[2.0]
For maximum value of A , the length of the rectangle represented by $y$ will be equal to:
