is it possible to construct a triangle with these given side lengths 6,10,15
Yes. Try it.
5 (or less),10 and 15 would not be possible side lengths.
Do you see why?
Yes it is
Yes, it is possible to construct a triangle with side lengths 6, 10, and 15. 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.
In this case, let's check if the given side lengths satisfy this theorem:
6 + 10 = 16 (greater than 15)
6 + 15 = 21 (greater than 10)
10 + 15 = 25 (greater than 6)
As all three sums are greater than the remaining side's length, it is possible to construct a triangle with side lengths 6, 10, and 15.
To determine if it is possible to construct a triangle with the given side lengths, we need to check if the sum of the two smaller sides is greater than the length of the longest side.
Let's sort the given side lengths in ascending order: 6, 10, 15.
The two smaller sides are 6 and 10, and the longest side is 15. Now, let's apply the triangle inequality theorem: the sum of the two smaller sides (6 + 10 = 16) should be greater than the length of the longest side (15). If this condition is satisfied, then it is possible to construct a triangle with the given side lengths.
In this case, 16 is greater than 15, so it is possible to construct a triangle with side lengths of 6, 10, and 15.