Question

Given the side lengths, determine whether the triangle is acute, right, obtuse, or not a triangle.

15, 16, 21
A Not a Triangle
B Acute
Obtuse
D Right

Answer 1

9514 1404 393

Answer:

B acute

Explanation:

We can define a "form factor" for a triangle as ...

f = a² +b² -c²

where c is the longest side length. It will be interpreted as follows:

• negative -- obtuse triangle
• zero -- right triangle
• positive -- acute triangle

For this triangle, our "form factor" is ...

f = 15² +16² -21² = 225 +256 -441 = 40 . . . . a positive number

The triangle is Acute.