Two sides of a triangle measure 9 cm and 23 cm. Which could be the measure of the third side of the triangle?
CLEAR SUBMIT
35 cm
32 cm
28 cm
4 cm
The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference of the other two sides.
In this case, the sum of the two given sides (9 cm and 23 cm) is 9 + 23 = 32 cm.
- 35 cm is longer than 32 cm, so it cannot be the measure of the third side.
- 32 cm is the same length as the sum of the two given sides, so it cannot be the measure of the third side.
- 28 cm is shorter than the sum of the two given sides, so it could be the measure of the third side.
- 4 cm is shorter than the difference of the two given sides, so it cannot be the measure of the third side.
Therefore, the measure of the third side could be 28 cm.
To determine which could be the measure of the third side of the triangle, we can apply 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.
Given that the lengths of the two sides are 9 cm and 23 cm, let's check if the third side can have a length of 35 cm:
9 + 23 = 32
32 is less than 35, so it satisfies the Triangle Inequality Theorem.
Now, let's check if the third side can have a length of 32 cm:
9 + 23 = 32
32 is equal to 32, so it satisfies the Triangle Inequality Theorem.
Next, let's check if the third side can have a length of 28 cm:
9 + 23 = 32
32 is greater than 28, so it satisfies the Triangle Inequality Theorem.
Finally, let's check if the third side can have a length of 4 cm:
9 + 23 = 32
32 is greater than 4, so it satisfies the Triangle Inequality Theorem.
Therefore, all four options could be the measure of the third side of the triangle.
To determine the possible measures of the third side of a triangle, we can make use of 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.
Given that two sides of the triangle measure 9 cm and 23 cm, we can apply the triangle inequality theorem to find the possible range of the third side's length.
Let's consider the maximum possible length for the third side. In this case, the sum of the two known sides (9 cm and 23 cm) would be equal to the length of the third side. So, the maximum length of the third side would be 9 + 23 = 32 cm.
Similarly, to find the minimum possible length for the third side, we subtract the two known sides instead of adding them. So, the minimum length of the third side would be |9 - 23| = 14 cm.
Based on these calculations, the possible measures for the third side of the triangle are between 14 cm and 32 cm. Therefore, among the options provided, the measure of 28 cm is within this range, and thus, it could be the measure of the third side of the triangle.