Calculate the sum of the lengths of the two sides and compare it with the length of the third side.
Yes, see solution.
Practice makes perfect
On the diagram we are given the measures of the triangle's sides.
By 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 find the sum of the lengths of each two sides and compare with the length of the third side.
Chose Two Sides
Sum
Third Side
Comparison
1 and 6 34
7 34
3 78
7 34 > 3 78
1 and 3 78
4 78
6 34
4 78 < 6 34
6 34 and 3 78
10 58
1
10 58 > 1
As we can see, the second sum does not satisfy the above theorem. Therefore, Catherine's concern was valid. A triangle with these measurements cannot exist.
