Question

The perimeter of a rectangle is 24 cm. What will be the length and breadth of that rectangle (In
whole numbers) for a) maximum area? b) the minimum area?

Answer 1

Answer:

The length would be 6cm and breadth would be 6cm because rectangles formally is 2 into length +breadth 6+6=12 into 2 = 24 cm

a)  the maximum area would be 36 cm

b) the minimum area would be 24 cm

IS THIS HELP FUII

Answer 2

Step-by-step explanation:

perimeter = 2(l+b) = 24

l+b=12

b=12-l

let A be the area of the rectangle

A=l×b

A=l×(12-l)

A=12l-l^2

Taking derivative both sides w.r.t l

= dA/dl = 12 - 2l —(i)

To find maxima or minima

12 - 2l = 0

= 2l = 12

= l = 6

Tking derievative of equation (i)

d^2A/dl^2 = -2

which is negative at l=6

So, A will be maximum at l = 6

Max Area = 6*(12-6) = 36 ( Remember:

1.all sqaures are rectangles also

2.a rectangle has maximum area when it is a square.)

and its minima is not defined.

As for area to be minimum, l -> 0 and we cannot define what exactly is value of l and thus there is no definite value of minimum area.

At l = 0, It becomes a line and cannot be said a rectangle.

As we need whole numbers, so, here the possible minimum area is when l = 1

Minimum Area = 1×11= 11.