Problems

Matt built a simple wooden hut to protect himself from the rain. From the side the hut looks like a right triangle with the right angle at the top. The longer part of the roof has \(20\) ft and the shorter one has \(15\) ft. What is the height of the hut in feet?

One day, Robinson Crusoe tied a rope tightly between two pegs, placed a sliding ring on it, and then tied the goat to the ring with another rope, as in the picture below. What shape did the goat graze this time?

On another day, Robinson Crusoe used two pegs again. This time, he tied one rope of length \(a\) to the first peg and another rope of length \(b\) to the second peg, both directly to the goat, so that it looked like in the picture below. What shape did the goat graze that day?

One day Robinson Crusoe decided to take his usual walk, and followed his path on a plateau holding his goat on the lead of 1 m length. Draw the shape of the area where the goat could have being eating grass while walking along Robinson Crusoe. The path they followed was exactly in the shape of 1 km\({}\times{}\)3 km rectangle.

Draw how Robinson Crusoe should put pegs and ropes to tie his goat in order for the goat to graze grass in the shape of a semicircle

In his twelfth year on the island Robinson Crusoe managed to tame a wolf, and used him as a guard dog for his goat. He used to tie the wolf with ropes to pegs and other ropes in such a way that there was always a safe place for the goat to escape. Subsequently, he studied the shapes the goat was grazing on the ground.
Draw a picture how Robinson used to tie the goat and the wolf in order for the goat to graze the grass in the shape of a ring

Think of other shapes Robinson’s goat can graze without a wolf, or with a wolf tied nearby. What if Robinson managed to tame several wolves and used them as guard dogs? Can two tied wolves keep an untied goat in a triangle? Can you think of other shapes you can create with Robinson’s goat and wolves?

A rectangle is made up from six squares. Find side length of the largest square if side length of the smallest square is 1.

This shape below is made up from squares.

Find side length of the bottom square if side length of the smallest square is equal to 1.