find the perimeter of a triangle if one side is 28 feet , another side is four-ninth the perimeter , and the third side is two-fifth the perimeter.

Assume that the perimeter is x

x = 28 + (4/9)x + (2/5)x
x(1 - 4/9 - 2/5) = 28

Solve the calculation above, and you'll get the answer

560 feet

To find the perimeter of a triangle, you need to add up the lengths of all three sides. Let's call the first side x.

From the given information, we know that the second side is four-ninths the perimeter, which can be expressed as (4/9)P, where P represents the perimeter.

Similarly, the third side is two-fifths the perimeter, which can be expressed as (2/5)P.

Therefore, the perimeter is the sum of these three sides: x + (4/9)P + (2/5)P.

We can simplify this expression by finding a common denominator for the fractions: 9 and 5 both divide evenly into 45, so we can rewrite the expression as x + (20/45)P + (18/45)P.

Now, we can simplify it further by combining the fractions: x + (38/45)P.

According to the information, one side is given as 28 feet, which means x = 28.

Now we can substitute x = 28 into our expression: 28 + (38/45)P.

To find the perimeter, we'll need to solve this equation. Since we don't have the exact value for P, we can leave it as it is or divide both sides by (38/45) to solve for P.

Perimeter = 28 + (38/45)P