Applications Of Derivatives Question 83
Question: The area of a rectangle will be maximum for the given perimeter, when rectangle is a
[AI CBSE 1991; RPET 1999]
Options:
A) Parallelogram
B) Trapezium
C) Square
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We know that perimeter of a rectangle $ S=2(x+y) $ , where x and y are adjacent sides
therefore $ y=\frac{S-2x}{2} $ .
Now area of rectangle, $ A=xy=\frac{x}{2}(S-2x)=\frac{1}{2}(Sx-2x^{2}) $
Differentiating w.r.t. x of A, we get $ \frac{dA}{dx}=\frac{1}{2}(S-4x)=0,\therefore x=\frac{S}{4} $ and $ y=\frac{S}{4} $
Again $ \frac{d^{2}A}{dx^{2}}=-ve $
Hence the area of rectangle will be maximum when rectangle is a square.
BETA
