determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles. 12 ft, 7 ft, 14 ft
a. unique triangle
b. many different triangles *****🤷🏽♀️
c. no triangles
Did you sketch more than one of them?
s,s,s conguent
You could turn it around or upside down or whatever, but same old triangle as far as I know.
What is the answer
To determine if the given side lengths can form a unique triangle, many different triangles, or no triangle at all, you can use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's apply this theorem to the given side lengths, which are 12 ft, 7 ft, and 14 ft.
Step 1: Sort the side lengths in ascending order:
7 ft, 12 ft, 14 ft
Step 2: Check if the two smallest side lengths (7 ft and 12 ft) are greater than the largest side length (14 ft):
7 ft + 12 ft = 19 ft > 14 ft
Since the sum of the two smallest side lengths is greater than the largest side length, the given side lengths satisfy the triangle inequality theorem.
Step 3: Check if any two side lengths are equal to the third side length:
No two side lengths (7 ft, 12 ft, and 14 ft) are equal.
Based on the triangle inequality theorem, we can conclude that the given side lengths can form a unique triangle. Therefore, the correct answer is option a. unique triangle.