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 went for a walk on a plateau, taking his goat with him on a rope of length one meter. He walked along a path in the shape of a rectangle measuring \(1 \,\text{km} \times 3 \,\text{km}\), following its perimeter. What was the shape of the area where the goat could graze while walking with Robinson?

Draw how Robinson Crusoe should use pegs, ropes, and sliding rings to tie his goat in order for the goat to graze grass in the shape of a semicircle.

Draw a picture how Robinson could have used pegs and ropes to tie the wolf and the goat so that the goat grazed an area in the shape of a ring (like a disc with a hole in the middle).

Can two tied wolves keep an untied goat in a triangle?

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.