Question

Is there any formula to solve it. Or we have to do by trial and error method only??
Q. If 10,14 and m are sides of an acute angled triangle, then how many integer values of m are possible?

Answer 1

it is solved without any formula

Answer 2

we know that triangle is only possible if the sum of the any two sides must be greater than or equal to the third side

but as it is acute angled triangle thus it must be only greater than and not equal to third side

sum of the sides =24
thus it can between 10 and 23
as it cannot be equal to 23 (in this case)
so that the above criterion is satisfied.

so there are 13 values.