How many different isosceles triangles can be made, if two of the sides must be 15 cm long and all sides must be an integer?
the 3rd side can't be zero ... no triangle
the 3rd side can't be greater than 29
... the two 15 sides wouldn't be long enough to close the triangle
the 3rd side can be any integer from one to twenty-nine
Sorry can you please explain how you got the answer as 29
To find how many different isosceles triangles can be made with two sides measuring 15 cm, we need to determine the possible lengths of the remaining side. In an isosceles triangle, the two equal sides are known as the legs, and the remaining side is called the base.
Since the two legs are equal and must measure 15 cm each, the base cannot be longer than 30 cm (15 cm + 15 cm). Additionally, the base cannot be shorter than the absolute difference between the two legs, i.e., |15 cm - 15 cm| = 0 cm.
Therefore, the possible lengths of the base can range from 1 cm to 29 cm, including both endpoints.
The number of different isosceles triangles is equivalent to the number of distinct base lengths that satisfy the conditions. In this case, the lengths of the base are integers, so we can count the number of integers between 1 and 29 (inclusive).
To find this count, we subtract the lower endpoint from the higher endpoint and add 1 to account for both endpoints:
Number of different isosceles triangles = (29 - 1) + 1 = 29
Therefore, there are 29 different isosceles triangles that can be made with two sides measuring 15 cm, where all sides are integers.