Question

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. what is the length, in inches, of the longest side of the triangle?

Answer 1

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

$16+2x+3x =66 \\ 16+5x = 66 \\ 5x = 50 \\ x =10$

So the other two sides are

$2*10, 3*10 \\ 20, 30$

And the length of the longest side is 30 inches .