A triangle has a perimeter of 30 ft. The first side is two more than twice the second side. The third side is one more than the first side. Find the length of each side.

Answer 1

If the sides lengths are a, b, and c, then a + b + c = 30

If the first side is 2 more than twice (2 times) the second side, then a = 2*b + 2

If the third side is 1 more than the first side, then c = a + 1

All of my equations involve an a, so I'm going to try to re-write equation 1 using only a.

1. Solve equation 2 for b in terms of a:
2. a = 2*b + 2
3. a - 2 = 2*b
4. b = (a-2) / 2 -> b = (1/2)*a - 1
5. We already know that c = a + 1
6. Substituting into the original equation:
7. a + b + c = 30
8. a + (1/2)a - 1 + a + 1 = 30
9. 2a + a - 2 + 2a + 2 = 60
10. 5a - 2 + 2 = 60
11. 5a = 60
12. a = 12

If a = 12 then:

1. Since b = (1/2)*a - 1 then b = (1/2)*12 - 1 = 5
2. Since c = a + 1, then c = 12 + 1 = 13

Therefore, the sides of our triangle are 5, 12, and 13

Answer 2

X + 2x+2 +2x+3=30

5x+5=30

5x=25

X=5

5,12,13