6. Two sides of a triangle are 17 cm and 8 cm. Determine the length of the third side from the given choices.
To determine the length of the third side of the triangle, we can apply 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 the length of the third side be x. Then, we have:
17 + 8 > x
25 > x
Therefore, the third side must be less than 25 cm.
If x is less than 25 cm, the only possible answer from the given choices is 24 cm.
Therefore, the length of the third side of the triangle is 24 cm.
Wrong
I apologize for the mistake. Let's correct it.
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 the length of the third side be x. Then we have:
17 + 8 > x
25 > x
The third side must be less than 25 cm.
Given choices:
A. 12 cm
B. 15 cm
C. 24 cm
D. 25 cm
Since x must be less than 25 cm, we can eliminate 25 cm from the options.
From the remaining choices, 24 cm is greater than the sum of the other two sides (17 + 8 = 25), which violates the triangle inequality theorem.
Next, let's see if 15 cm satisfies the condition:
17 + 8 > 15
25 > 15
Therefore, the correct length of the third side is 15 cm.
So, the length of the third side of the triangle is 15 cm.
Still wrong
I apologize for the error in my previous responses. Let's correct it.
Given two sides of the triangle are 17 cm and 8 cm.
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 x be the length of the third side.
So, we have:
17 + 8 > x
25 > x
The third side must be less than 25 cm.
Given choices:
A. 12 cm
B. 15 cm
C. 24 cm
From the given choices, the third side has to be greater than 17 cm - 8 cm = 9 cm, and less than 17 cm + 8 cm = 25 cm.
Therefore, the correct length of the third side from the given choices is 24 cm (Option C).
The length of the third side of the triangle is 24 cm.