Question

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers and together form a pythagorean triple. Find the length of the third side, and tell whether it is a leg or a hypotenuse.
2 Given length: 24, 51
A.
21 leg
B.
45 leg
C.
48 leg
D.
56 hypotenuse

Answer 1

If all three side lengths are INTEGERS and form PYTHAGOREAN TRIPLE then we know decimals are not allowed

if 24 and 51 are both legs then
$24^{2} + 51^{2} = x^{2}$
x = 3177
and squre root of that gives us 56.364.... NOT an integer

So that means one of them is not a leg and since hypotenuse is longer than both legs, 51 must be the hypotenuse so to get the third side

$51^{2} - 24^{2} = x^{2}[tex] [tex] x^{2}$=2025
x=45, leg B