Question

in a triangle with integer side lengths one is three times as long as second side and the length of the third side is 17.what is the greatest possible perimeter?

Answer 1

If the second side has length x,

Then the first side has length 3x,

We know that the third side which has length 17.

Now, by the triangle inequality, we have:

x + 17 > 3x

=> 2x < 17

=> x < 8.5

Since we want the greatest perimeter,so we need the greatest integer x, and if x < 8.5.

Then x = 8

Then, the first side has length -> 3 x 8 = 24

The second side has length = 8 cm

The third side has length = 17 cm

So,perimeter = 17 + 24 + 8 = 49 cm