Question

B. BUILD PERSEVERANCE The lengths of the sides of an isosceles triangle are whole numbers, and the perimeter of the triangle is 30 units. What is the probability that the triangle is(equilateral?​

Answer 1

1/7

Explanation:

it can only work, if the baseline is shorter than 15 units (half of the 30 units perimeter), because if it is longer, then the sides (or legs) cannot be long enough to connect to each other and to the ends of the baseline. and so, it would not be a triangle anymore.

so, there are 14 possible whole number cases for such baselines (baseline is 14, 13, 12, ..., 2, 1 units long), but only 7 of them allow the sides to be equally long with whole number lengths.

because if the baseline was e.g. 13 units long, then each side would have to be

(30 - 13)/2 = 17/2 = 8.5 units long (not a whole number).

so, the valid baseline lengths are 14, 12, 10, 8, 6, 4, 2 units.

that are 7 possible cases.

but only one of these cases would make it an equilateral triangle (all 3 sides are equally long) : 30/3 = 10 units per side.

so, the probability is (desired cases / total cases)

1/7