Emily drew the following triangle. Does such a triangle exist?
A triangle with side lengths 12 in., 15 in., and 20 in. is shown. A right angle symbol is shown in the angle formed by the sides of lengths 12 in. and 15 in.
Yes, it is possible to create a right triangle with the side lengths shown.
No, it is not possible to create a right triangle with the side lengths shown.
No, it is not possible to create a triangle with the side lengths shown.
Yes, it is possible to create a right triangle with the side lengths shown.
Yes, it is possible to create a right triangle with the side lengths 12 in., 15 in., and 20 in.
To determine if a triangle can be formed with the given side lengths, we need to check if it satisfies the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's check if the given side lengths satisfy the triangle inequality theorem:
- The sum of the lengths of the sides with lengths 12 in. and 15 in. is 12 + 15 = 27 in.
- The length of the third side is given as 20 in.
Since 27 in. is greater than 20 in., we know that the triangle inequality theorem is satisfied.
Additionally, you mentioned that a right angle symbol is shown in the angle formed by the sides of lengths 12 in. and 15 in. This corresponds to a right triangle.
Therefore, it is indeed possible to create a triangle with the given side lengths.