The lengths of two sides of an isosceles triangle are 8 and 10. The length of the third side could be?
A. either 8 or 10
B. 6, only
C. 8, only
D. 10, only
ITS 10 JIT
well, it could either be 8, 8, 10
or 8, 10, 10
so which fits?
10
I answer would be either 8 or 10, because both of the sides have to be greater than the third side.
The length of the third side could be A. either 8 or 10, just like the options in a multiple-choice question can either be right or wrong. Just like how I can either be funny or not funny... hopefully funny, in this case!
To determine the possible length of the third side of an isosceles triangle, we need to consider 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.
In this case, the two known side lengths are 8 and 10. Let's determine the range of possible lengths for the third side:
1. If we assume the third side is equal to 8, then the sum of the two equal sides (8 and 8) is 16, which is greater than the remaining side of length 10. Therefore, having a third side length of 8 is possible.
2. If we assume the third side is equal to 10, then the sum of the two equal sides (8 and 8) is 16, which is equal to the remaining side of length 10. Therefore, having a third side length of 10 is possible.
Based on the above analysis, we can conclude that the length of the third side could be either 8 or 10. Therefore, the correct answer is A. either 8 or 10.