Applications Of Derivatives Question 304
Question: The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are
[MP PET 1993]
Options:
A) 10 cm and 40 cm
B) 20 cm and 30 cm
C) 25 cm and 25 cm
D) 15 cm and 35 cm
Show Answer
Answer:
Correct Answer: C
Solution:
$ 2x+2y=100\Rightarrow x+y=50 $ …………..(i)
Let area of rectangle is A;
$ \therefore A=xy\Rightarrow y=\frac{A}{x} $
Put in (i), we have $ x+\frac{A}{x}=50\Rightarrow A=50x-x^{2} $
therefore $ \frac{dA}{dx}=50-2x $
For maximum area $ \frac{dA}{dx}=0 $
$ \therefore 50-2x=0\Rightarrow x=25 $ and $ y=25 $
Hence adjacent sides are 25 and 25 cm.
BETA
