Is it a right triangle if the sides of given lengths are 5in., 10in., 12in. ?

The if the legs of a right triangle are a and b and the hyponuse (longest side) is c then
a²+b²=c²

so
12 is biggest so it is c

5²+10²=12² should be true if it is a right triangle
25+100=144?
125=144?
no
not a right triangle