Question

The pesrmeter of Rectangle is 100 em find the dimension when ite area is maximum​

Answer 1

Let l and b are the sides of rectangle.

$\therefore \: 2(l + b) = 100$

$l + b = 50 - - - - - (1)$

If the area of rectangle is A, then

A=l×b

l(50-l) [From eq. (1)]

$50 \: l - {l}^{2}$

$= > \frac{dA}{dl} = 50 - 2l$

$For \: maxima/minima$

$\frac{dA}{dl} = 0$

$= > 50 - 2l = 0 \\ = > l = 25 \: cm \\ and \: \frac{ {d}^{2}A }{d {l}^{2} } = - 2 < 0$

∴At l=50cm, is maximum.

Therefore, for maximum area, the sides of rectangle are 50 cm and 50 cm.