Question

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

Answer 1

9514 1404 393

Answer:

  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.)