Question

In ΔKLM, LM = 5, MK = 12, and KL = 10. Which statement about the sides of ΔABC must be true?

Answer 1

Applying the Pythagorean theorem to ΔKLM with sides 5, 10, and 12, it is determined that the triangle is not a right triangle because the sum of the squares of the two shorter sides does not equal the square of the longest side.

Step-by-step explanation:

In ΔKLM, where LM = 5, MK = 12, and KL = 10, we can apply the Pythagorean theorem because the side lengths suggest that ΔKLM could be a right triangle. If ΔKLM is a right triangle, by the Pythagorean theorem, the sum of the squares of the two shorter sides (5 and 10) should equal the square of the longest side (12). Calculating 52 + 102 gives us 25 + 100 = 125, which is indeed equal to 122 (144), indicating that our initial assumption is incorrect and ΔKLM is not a right triangle.