Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point).
According to the triangle inequality 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 consider the two given sides: 4 cm and 9 cm.
The length of the third side (hypotenuse) in a right triangle can be determined using the Pythagorean theorem:
a² + b² = c², where a and b are the lengths of the two legs, and c is the length of the hypotenuse.
Using the Pythagorean theorem:
4² + 9² = c²
16 + 81 = c²
97 = c²
c ≈ 9.849 cm
Therefore, the measure of the third side (hypotenuse) cannot be 10 cm because it is greater than the calculated approximate value of 9.849 cm.
Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point)
To determine the length of the third side, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider the two given sides: 10 and 12.
Using the triangle inequality theorem:
10 + 12 > x, where x is the length of the third side.
10 + 12 = 22
Therefore, the length of the third side must be greater than 22.
None of the choices provided, the length of the third side, are greater than 22 cm.
Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point)
Your closest answers are 10 and 9 right now, which one?
Apologies for the confusion. In the given triangle with sides measuring 4 cm and 9 cm, let's consider the two choices you provided: 10 cm and 9 cm for the third side.
Using the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the choice 10 cm:
4 + 9 = 13, which is greater than 10 cm. Therefore, 10 cm can indeed be the measure of the third side.
For the choice 9 cm:
4 + 9 = 13, which is equal to 13 cm. Since 13 cm is equal to the sum of the other two sides, 9 cm cannot be the measure of the third side.
Therefore, out of the two choices provided, 9 cm cannot be the measure of the third side.
Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point) Responses
According to the triangle inequality 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 consider the two given sides: 4 and 6.
Using the triangle inequality theorem, we can evaluate the choices provided:
Option 1: 2
4 + 2 = 6, which is equal to 6. Since 6 is not greater than 2, option 1 cannot be the measure of the third side.
Option 2: 7
4 + 7 = 11, which is greater than 6. Therefore, option 2 (7) could be the measure of the third side.
Option 3: 9
4 + 9 = 13, which is greater than 6. Therefore, option 3 (9) could be the measure of the third side.
Option 4: 10
4 + 10 = 14, which is greater than 6. Therefore, option 4 (10) could be the measure of the third side.
Based on the evaluation, options 2, 3, and 4 could be the measure of the third side of a triangle if the first two sides measure 4 and 6.