Question

The perimeter of a rectangle is 40 m. If the sides of the rectangle are natural numbers,
find the dimensions of the rectangle having the maximum area. please explain properly

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Answer 1

Answer:

Let l and b are the sides of rectangle.

∴2(l+b)=40

⇒l+b=20 …(1)

If the area of rectangle is A, then

A=l⋅b

l(20−l) [From eq. (1)]

=20l−l2

⇒dAdl=20−2l

For maxima/minima

dAdl=0

⇒20−2l=0

⇒l=10cm

And d2Adl2=−2<0

∴ At l=10cm, is maximum.

Therefore, for maximum area, the sides of rectangle are 10 cm and 10 cm.