Question

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

Answer 1

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

Answer 2

In a right triangle, the hypotenuse is 5 units long.

let other sides be a and b

a, b < 5 as 5 is hypotenuse

and a^2 + b^2 = 5^2 for right triangle

the legs also have integer lengths so a and b are integers

a and b can only be 1, 2, 3 or 4

by trial and error, a, b are 3 and 4