A triangle has side lengths of 3 ft., 5 ft., 4 ft. How many triangles are possible?
only one: a right triangle.
Thanks!
To determine how many triangles are possible with the given side lengths, we need to check if they satisfy the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Let's consider the side lengths given: 3 ft., 5 ft., and 4 ft.
To find out if these side lengths can form a triangle, we can apply the triangle inequality theorem to each pair of sides:
1. 3 ft. + 5 ft. > 4 ft.
8 ft. > 4 ft. (true)
2. 3 ft. + 4 ft. > 5 ft.
7 ft. > 5 ft. (true)
3. 4 ft. + 5 ft. > 3 ft.
9 ft. > 3 ft. (true)
Since all three conditions are satisfied, the given side lengths can form a triangle. Therefore, only one triangle is possible with side lengths of 3 ft., 5 ft., and 4 ft.