D, C, A nad then B
Figure out the number of possible triangles that fit condition A. There are 3 possible combinations of three even numbers that sum to 12.Of these three, there is only one where every length is less than the sum of the other two: 4 inches,4 inches, 4 inches. So, there is only one triangle that fits condition A.Figure out the number of possible triangles that fit condition B. Since the perimeter and two side lengths are given, subtract the two side lengths from the perimeter to get the length of the third side.Sketch a triangle with lengths of 2 inches, 4 inches, and 5 inches.From the sketch, the angle between the 4-inch length and 5-inch length has to be the smallest angle. Since it has to be the smallest angle, it cannot be more than a right angle. So, there is zero triangles that fit condition B.Figure out the number of possible triangles that fit condition C. For the area to be less than13 square inches, the product of the legs must be less than 26 square inches. The right triangles with odd-numbered legs greater than 1 inch whose product is less than 26 square inches are shown below.So, three triangles fit condition C.Figure out the number of possible triangles that fit condition D. If two angles of an isosceles triangle measure 50º, the third can be found by subtraction both angle measures from 180º.So, the angle measures must be 50º, 50º, and 80º. There is no condition on the lengths, so there are an infinite number of triangles that fit condition D.Therefore, the conditions in order of greatest possible triangles to least are shown below.condition D, condition C, condition A, condition B
