It is given in the question that,
A triangle with a perimeter of 66 inches has one side that is 16 inches long. the length of the other two sides have a ratio of 2:3.
Let the other two sides are of length 2x and 3x respectively .
And perimeter is the sum of the lengths of all three sides, that is
[tex] 16+2x+3x =66
\\
16+5x = 66
\\
5x = 50
\\ x =10 [/tex]
So the other two sides are
[tex] 2*10, 3*10
\\
20, 30 [/tex]
And the length of the longest side is 30 inches .
