Lesson 3. A Farmer's Good Fortune

 

Long ago there lived a farmer. He had a small piece of land and he was very poor. His land was a square only 100 meters on each side.

"Oh !" said the farmer, "I wish I had a bigger piece of land."

One day an old man came to the farmer's house. He looked very poor and hungry.

The old man said to the farmer, "Please give me something to eat."

The farmer was poor, but he was very kind. He gave the old man a piece of bread and a glass of cold milk. It was all the food he had.

"It's so kind of you to help me," said the old man. When he finished the bread and milk, a strange and a handsome gentleman appeared in his place.

"I am your king," he said. "You were kind to me. I'll gave you some land."

The farmer was surprised. He didn't know how to thank the king.

"You may double the size of your land," the king added. "But it must still be in the shape of a perfect square."

Now the farmer could plant twice as much. He would have enough food for his family ! He hurried out to measure his land.

But there was a problem. At first the farmer thought each side of the square should be doubled. But this didn't work !

The new square was four time as big as the old one.

The farmer got some paper and a pencil. He drew a square and looked at it.

 

"Hmmmm," he said to himself, "I can divide this big square into four little squares all the same size."

 

His drawing looked like this.

He thought, "I can add four little squares."

 

First he tried this. But it was not a square. He cried, "This is impossible !"

 

But he did not give up.

He tried again and again.

Once he did this. It almost worked. But it wasn't a square. The corner was missing.

"I'm afraid I can't double the size of my land after all," he said.

"If I fail to solve this problem, my family will not have enough to eat."

Then suddenly he got another idea ! Finally he solved the problem.

Can you figure it out? After you think you have solved the problem, look at the following picture. Is your answer the same as the farmer's?

 

Dialogue(1)

In-suk : Would you do me a favor?

Yu-mi : What is it?

In-suk : It's not easy for me to understand this. Can you explain it to me?

Yu-mi : Sure. He made a diamond by adding four little triangles.

In-suk : Oh ! Now I understand. It's so kind of you to help me.

Yu-mi : No problem.

 

Dialogue(2)

A Man : Excuse me. Could you tell me where the nearest subway station is?

Mike : I'm sorry, I'm a stranger here myself. Do you know where it is, Sang-ho?

Sang-ho : Yes. Go straight ahead and turn right. It is just beyond the bank.

A Man : Should I cross the street?

Sang-ho : No, you don't have to.

There's an entrance on this side.