1. When I visited the professor's house, his gardener was pushing an old hand-mower where vegetables used to grow. "That lawn's new," I commented. "A right-angled triangle with straight sides, all right, but what a funny shape for a lawn." "It's the professor's idea," said the gardener. "The sides are all exact metres. He says the perimeter is a perfect cube, and the smallest one that will work." What were the dimensions of that lawn?

Lawn 90 by 72 by 54 metres.

Lawn 80 by 62 by 55 metres.

Lawn 95 by 78 by 61 metres.