Question

if one side triangle is one-third the perimeter , the second is one -fourth the perimeter , and the third is 7 meters, What is the perimeter of the triangle ?

Answer 1

P = Perimeter

P = a + b + c

a = P / 3

b = P / 4

P = a + b + c = P / 3 + P / 4 + 7



P / 3 = 4 P / 12

P / 4 = 3 P / 12



P = P / 3 + P / 4 + 7

P = 4 P / 12 + 3 P / 12 + 7

P = 7 P / 12 + 7

P - 7 P / 12 = 7

12 P / 12 - 7 P / 12 = 7

5 P / 12 = 7 Multiply both sides with 12

5 P = 7 * 12

5 P = 84 Divide both sides with 5

P = 84 / 5

P = 16.8 m

Answer 2

Let the sides be a, b and 7
Perimeter = a+b+7

a = (1/3)(a+b+7)
3a = a+b+7
2a - b = 7

b = (1/4)(a+b+7)
4a = a+b+7
3a -b = 7
subtract ---- a = 0
then b = -7
Answers make no sense

following "anonymous' " solution
P = a+b+7
a= P/3
b = P/4
P = P/3 + P/4 + 6
times 12
12P = 4P + 3P + 84
5P = 84
P = 16.8

So , one side should be (1/3)(16.8) or 5.6 , which would leave 4.2 for the 2nd side,
but 4.2 ≠ (1/4)(16.8)

Thus there is really no solution which satisfies all conditions.
This question has contradictory data and thus is bogus.

Answer 3

Eh? Looks like 16.8/4 = 4.2

Also, there's a typo in your solution, unfortunately:

b = (1/4)(a+b+7)
4a = a+b+7
3a -b = 7

should be

4b = a+b+7
-a + 3b = 7

And, in fact,

b = 4.2
a = 5.6