Question

Construct rectangle whose perimeter is 400 cm such that it has a maximum area

Answer 1

Let the sides of the rectangle be x and y

Perimeter = 2(x+y) 400

x+y=200

y=200-x

So, the rectangle has sides x and 200-x

A = x(200-x)

A= 200x - x²

At maximum area dA/dx = 0

dA/dx = 200-2x

200-2x=0

-2x=-200

x = 100

y = 200-100 = 100

So, this is actually a square of sides 100 cm

Using a scale of 1 cm rep. 20 cm, the square can be constructed as shown in the image attached.

Answer 2

Answer:

Step-by-step explanation:

Let the sides of the rectangle be x and y

Perimeter = 2(x+y) 400

x+y=200

y=200-x

So, the rectangle has sides x and 200-x

A = x(200-x)

A= 200x - x²

At maximum area dA/dx = 0

dA/dx = 200-2x

200-2x=0

-2x=-200

x = 100

y = 200-100 = 100

So, this is actually a square of sides 100 cm

Using a scale of 1 cm rep. 20 cm, the square can be constructed as shown in the image attached.