Determine if the following lengths could represent a triangle. If they can, determine if the triangle, is acute, obtuse, or right. A. 5, 8, 13
B. 7, 12, 26
C. 11, 15, 20

9514 1404 393

  A. no

  B. no

  C. obtuse

Step-by-step explanation:

For side lengths to form a triangle, the sum of the shorter two must exceed the longest.

A. 5 + 8 = 13 . . . . a line segment, not a triangle

B. 7 + 12 < 26 . . . . no closure, not a triangle

C. 11 + 15 > 20 . . . . a triangle. A picture shows it to be obtuse

  You can also compare 11² +15² vs 20² ⇒ 346 vs 400. The long side is too long for a right triangle, so the triangle must be obtuse. (The Pythagorean theorem tells you a right triangle with those legs would have a long side of √346 = 18.6.)