A triangle has side lengths of 7 cm, 1 cm, 9 cm. How many triangles are possible?
none. each side must be less than the sum of the other two.
9 is too long. The sides of 7 and 1, laid down completely flat don't reach from one end to the other.
A triangle has side lengths of:
6 inches
6 inches
Any length less than 12 inches.
How many triangles are possible?
To determine how many triangles are possible with the given side lengths, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Let's consider the different combinations of sides possible:
Combination 1: 7 cm + 1 cm = 8 cm < 9 cm (not possible)
Combination 2: 7 cm + 9 cm = 16 cm > 1 cm (possible)
Combination 3: 1 cm + 9 cm = 10 cm > 7 cm (possible)
From the above combinations, we can conclude that two triangles are possible with side lengths of 7 cm, 1 cm, and 9 cm.
To determine how many triangles are possible with these side lengths, we need to check if they satisfy 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.
Let's go through the possibilities for the given side lengths:
1. The sum of 7 cm and 1 cm is 8 cm, which is greater than 9 cm. The sum of 7 cm and 9 cm is 16 cm, which is greater than 1 cm. The sum of 1 cm and 9 cm is 10 cm, which is greater than 7 cm. Since all three combinations of side lengths satisfy the triangle inequality theorem, a triangle is possible in this case.
Therefore, there is only one triangle possible with the given side lengths.