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 ?

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

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.

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

To find the perimeter of the triangle, we need to first determine the lengths of the other two sides.

Let's assume the perimeter of the triangle is "P" meters.

According to the given information, one side of the triangle is one-third the perimeter, which means its length is P/3 meters.

Similarly, the second side of the triangle is one-fourth the perimeter, so its length is P/4 meters.

The third side of the triangle is given as 7 meters.

To find the perimeter, we add up the lengths of all three sides:

P = P/3 + P/4 + 7

To simplify the equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12.

12P = 4P + 3P + 84

Combining like terms, we get:

12P = 7P + 84

Subtracting 7P from both sides:

12P - 7P = 84

5P = 84

Finally, dividing both sides by 5:

P = 84/5

Therefore, the perimeter of the triangle is 16.8 meters.