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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

User Duefectu
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3.8k points

1 Answer

3 votes

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.

Given the side lengths, determine whether the triangle is acute, right, obtuse, or-example-1
User ColinYounger
by
3.2k points