Question

Using Pythagorean inequalities, determine which set of the given three sides produces an obtuse triangle. A. 4, 5, 6 B. 5, 13, 19 C. 12, 14, 25 D. 21, 72, 75

Answer 1

c

Explanation:

just did it

Answer 2

Obtuse triangle sets

B. 5, 13, 19

C. 12, 14, 25

Explanation:

The Pythagorean inequality for the sides of the triangle to be an obtuse:

`a^2 + b^2 < c^2`, where a, b and c are the sides of the triangle.

The other Pythagorean inequalities are:

`a^2 + b^2 > c^2`, for Acute triangle

`a^2 + b^2 = c^2`, for Right triangle

Now let's check which set of the given sets satisfy the above inequality.

Option A

4, 5, 6

Here a = 4, b = 5 and c = 6

`4^2 + 5^2 < 6^2\\16 + 25 < 36\\41 < 36\\`

Which is not true.

Here
`a^2 + b^2 > c^2`, So this is Acute triangle

Option B

5, 13, 19

Here a = 5, b = 13 and c = 19

`5^2 + 13^2 < 19^2\\25 + 169 < 361\\194 < 361\\`

Which is true. This is Obtuse triangle

Option C

Here a = 12, b = 14 and c = 25

`12^2 + 14^2 < 25^2\\144 + 196 < 625\\340 < 625\\`

Which is true. This is obtuse triangle.

Option D

Here a = 21, b = 72 and c = 75

`21^2 + 72^2 < 75^2\\441 + 5184 < 5625\\5625 < 5625\\`

Which is not true for obtuse.

Here
`a^2 + b^2 = c^2`, for Right triangle

So this is Right triangle.