Question

in a triangle 30a + 6b = 5c . find  a, b, c

Answer 1

GIVEN,  5c = 30 a + 6 b, DIVIDE by 5 to get

c = 6 a + 1.2 b
c  = (a + b)  + (5a +0.2b)
c > a + b

a and b are always positive.  It means that c > a+b that means it is not a triangle.  If c < a+b then it can be a triangle. In a triangle sum of two sides is always greater than the third.

A triangle is not possible with the above relation among the sides.

Answer 2

30a + 6b = 5c

First of all, note that 5 * 6 = 30, so what we can assume is,
a = x
b = 5y

Then,
5c = 30x + 30y
c = 6(x + y)
c = 6x + 6y
for x, y > 0


Now check the triangular inequality,
(1) a + b > c, this gives 5x + y < 0
(2) a + c > b, this gives 7x + y > 0
(3) b + c > a, this gives 5x + 11y > 0

Now inequality (1) has no solution for x, y > 0

Thus, NO Triangle Possible ...