Question

The dimensions of a rectangle of maximum area inscribed in a semi circle of radius 8 cms is

• A. $8\sqrt{2},4\sqrt{2}$
• B. $8\sqrt{2},8\sqrt{2}$
• C. $4\sqrt{2},4\sqrt{2}$
• D. $4\sqrt{2},\sqrt{2}$

Answer 1

The correct option is A $8\sqrt{2},4\sqrt{2}$

Let vertices be $(8sin\theta ,8cos\theta ),(-8sin\theta ,8cos\theta )$
$(-8sin\theta ,0)(8sin\theta ,0)$
area of rectangle $=16sin\theta \times 8cos\theta$
$=64si{n}^2\theta$
area is max when $\theta =\frac{\pi }{4}$
So side are $=16sin\theta ,8cos\theta$
$=8\sqrt{2},4\sqrt{2}$