Given that 2a = 5b = 6c, we can set up ratios to find the value of a:b:c.

Let’s start by equating pairs of these ratios:

2a = 5b ⇒ a/b = 5/2

5b = 6c ⇒ b/c = 6/5

Now, since we have a ratio for a:b and a ratio for b:c, we can combine these ratios to find a:b:c:

a/b = 5/2

b/c = 6/5

We can use the transitive property of ratios to equate a/c:

a/b * b/c = a/c

Substitute the given ratios:

(5/2) * (6/5) = a/c

The b terms cancel out:

3 = a/c

So, the value of the ratio a:b:c is 3:5:2.