Question

The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are

• A. 10 cm and 40 cm
• B. 20 cm and 30 cm
• C. 25 cm and 25 cm
• D. 15 cm and 35 cm

Answer 1

The correct option is C 25 cm and 25 cm

Let x and y be the adjacent sides of the rectangle.

perimeter of the rectangle $=100cm$

$2(x+y)=100$

$(x+y)=50$

Area of the rectangle $=x\times y$

$A=x(50-x)$

$A=50x-x^2$

for maximum area,$\frac{dA}{dx}=0$

$50-2x=0$

$2x=50$

$x=25$

$y=50-x$

$y=50-25$

$y=25$

The adjacent sides of a rectangle enclosing maximum area are 25cm and 25cm