Question

The King was very happy with carpenters Cheggu and Anar. They had made a very big and beautiful bed for him. So as gifts the king wanted to give some land to Cheggu, and some gold to Anar.
Cheggu was happy. He took 100 metres of wire and tried to make different rectangles.
He made a 10 m × 40 m rectangle.
Its area was 400 square metres.
So he next made a 30 m × 20 m rectangle.
• What is its area? Is it more than the first rectangle?
• What other rectangles can he make with 100 metres of wire? Discuss which of these rectangles will have the biggest area.
Cheggu's wife asked him to make a circle with the wire. She knew it had an area of 800 square metres.
• Why did Cheggu not choose a rectangle? Explain.
So Anar also tried many different ways to make a boundary for 800 square metres of land.
• He made rectangles A, B and C of different sizes.
Find out the length of the boundary of each. How much gold wire will he get for these rectangles?

A

B

C

But then Anar made an even longer rectangle...... See how long!

D
So he will get __________ metres of gold wire!!

Answer 1

• Area of 30 m × 20 m rectangle = 600 square metres

Its area is larger than the area of first rectangle.

• The other rectangles that he can make with 100 metres of wire are

40 m × 10 m, 48 m × 2 m, 49 m × 1 m, 45 m × 5 m

A



As the area of rectangle A is shown as 40 m $\times$ 20 m.
So, the length of rectangle = 40 m
Width of rectangle = 20 m

Gold wire for A = 40 + 20 + 40 + 20 = 120 metres

B

As the area of rectangle B is shown as 80 m $\times$ 10 m.
So, the length of rectangle = 80 m
Width of rectangle = 10 m

Gold wire for B = 80 + 10 + 80 + 10 = 180 metres

C

As the area of rectangle C is shown as 800 m $\times$ 1 m.
So, the length of rectangle = 800 m
Width of rectangle = 1 m

Gold wire for C = 800 + 1 + 800 + 1 = 1602 metres

D

As the area of rectangle D is shown as 8000 m $\times$ 0.1 m.
So, the length of rectangle = 8000 m
Width of rectangle = 0.1 m
Gold wire for C = 8000 + 0.1 + 8000 + 0.1 = 16000 + 0.2 = 16000.2 metres.
So, he will get 16000.2 metres of gold wire!!