The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side if the perimeter is not more than 120 inches.

Answer 1

If the sides are in ratios of 5:12:13 then you could say the sides are 5x, 12x, and 13x. Add these together to get the perimeter. so the perimeter is 30x. But you know that the "not more than 120 inches" so we could say it is < 120. So:

30x < 120

or x < 4

The shortest side is 5x so if x < 4, then 5x < 20 so the shortest side is less than or equal to 20 (but of course, greater than 0)