self Maths Puzzle

The clown after juggling with the five triangular pieces of cardboard to attract attention proceeds to cut one of them into two pieces.

He then lays the six pieces upon the top of the box and shows that they will fit together and form a perfect square.

The pieces represent five right-angled triangles, say one inch high by two inches on the base, so you can readily cut five similar pieces from paper and then guess how to cut one of them so that the six pieces will form a perfect square.

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self Other Question

Here is a pretty puzzle from Mother Goose's story of Jack and Jill's race for a pail of water.

The distance to the top of the hill was 440 yards, which is just a quarter of a mile.

Jack got to the top first and was 20 yards on the return trip when he met Jill whom he beat home by half a minute.

The record of the race is complicated by the runners being able to run down hill one-half again faster than they ran up, so you are asked to figure out Jack's time for the half mile run.
Bluebeard explains that his bunch of keys was strung upon an endless key ring and divided into three groups so that the first group multiplied by the second equaled the third!

That was the secret by which he knew whether the keys had been tampered with and forbidden chambers had been entered.

You see that 6910 multiplied by 7 does not amount to 83452, so the keys were not replaced properly in their groups.

Can our clever puzzlists show how the keys must have been arranged in three groups so that the first group multiplied by the second makes the third?