Question

A rectangle has an area 50 St-cm Find
its dimensions for least perimeteę.​

Answer 1

Step-by-step explanation:

Area of a rectangle =50cm

2

let the length be x

and breadth be y

∴ xy=50⟶(1)

Now, perimeter =2x+2y⟶(2)

From (1),

x=50/y⟶(3)

Substituting (3) in (2) we get

P=2(

y

50

)+2y

=

y

100

+2y

∴

dy

dP

=

y

2

−100

+2=0

⇒2=

y

2

100

⇒y=

50

=5

2

cm

∴ x=5

2

cm

∴ For the perimeter to be least for a given area the rectangle would have

Answer 2

Answer:

Area of a rectangle =50cm

2

let the length be x

and breadth be y

∴ xy=50⟶(1)

Now, perimeter =2x+2y⟶(2)

From (1),

x=50/y⟶(3)

Substituting (3) in (2) we get

P=2(

y

50

)+2y

=

y

100

+2y

∴

dy

dP

=

y

2

−100

+2=0

⇒2=

y

2

100

⇒y=

50

=5

2

cm

∴ x=5

2

cm

∴ For the perimeter to be least for a given area the rectangle would have to be a square.