2 sides of a triangle are consecutive odd integers. The third side is twice as long as the shortest side. The perimeter is 22. Find the length of the shortest side.

Question

2 sides of a triangle are consecutive odd integers. The third side is twice as long as the shortest side. The perimeter is 22. Find the length of the shortest side.

I guessed
A+b+c=22 and that's as far as I got

Answer 1

You were right as far as you went. But, you didn't use the rest of the information they gave you.

a+b+c = 22

But what else do we know?
If a is the short side (assuming it is indeed an odd integer), then

b=a+2 (next odd integer)
c=2a (twice as big)

So, substituting in the given information,

a+b+c = 22
a + a+2 + 2a = 22
4a+2 = 22
4a = 20
a = 5

So, the sides are 5,7,10