In a right triangle, the hypotenuse is 5 units long, and the legs also have integer lengths. How long are the legs?

Note:How many different cases are there?

A^2 + b^2 = c^2 for a right triangle

c=5 so a^2 + b^2 = 5^2 = 25

a n b are integers

a n b must be < 5 cuz' hypotenuse is the longest

so a n b can only be 2 cases: 3,4 or 4,3

5^2 = a^2 + b^2

25 = a^2 + b^2

the other sides need to be shorter than 5 so plug them and and see what works:

25 = 4^2 + 4^2 = 25 = 16+16 = 25 = 32 false

25 = 4^2 + 3^2 = 16+9 = 25, 25 = 25 True

the only one that works would be sides of 3 and 4 units long