The length of the first side of a triangle is 12 units. The length of the second side is 5/9 the length of the first side. Find the perimeter of the triangle if 6/5 of the length of the third side equals the length of the first side.
The length of the second side is 5/9 * 12 = <<5/9*12=6.666666666666667>>6.67 units
The length of the third side is 5/6 * 12 = 10 units
The perimeter of the triangle is 12 + 6.67 + 10 = <<12+6.67+10=28.67>>28.67 units. Answer: \boxed{28.67}.
To find the perimeter of the triangle, we need to know the length of all three sides.
Let's start by finding the length of the second side. We are given that the second side is 5/9 the length of the first side.
Length of second side = (5/9) * 12 units
Length of second side = 20/3 units
Next, let's find the length of the third side. We are given that 6/5 of the length of the third side equals the length of the first side.
Length of third side = (6/5) * 12 units
Length of third side = 72/5 units
Finally, we can find the perimeter of the triangle by adding up the length of all three sides.
Perimeter = Length of first side + Length of second side + Length of third side
Perimeter = 12 units + 20/3 units + 72/5 units
To add these fractions, we need to find a common denominator.
Perimeter = (12 * 15/15) units + (20/3 * 5/5) units + (72/5 * 3/3) units
Perimeter = 180/15 + 100/15 + 216/15 units
Perimeter = 496/15 units
Therefore, the perimeter of the triangle is 496/15 units.