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How many right-angled triangles are there with sides that are all integers less than 100 units?

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A square patio was tiled with square tiles all the same size. Some of the tiles were removed from the middle of the patio in order to make a square flower bed, but the number of the remaining tiles was still a square number. What were the dimensions of the patio and the flower bed?

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Paving the Way

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

If the number of tiles used originally was x 2 and the total number of tiles used was y 2 , then :

x 2 + 100 = y 2
x 2 + 10 2 = y 2

This is a Pythagorean triple (see Pythagorean Triples ) which can be satisfied by x = 24 with y = 26.
So total number of tiles = 26 2 = 676

Correct solution from Adrian from South Greenhoe Middle School.