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

Answer:

Obtuse triangle sets

B. 5, 13, 19

C. 12, 14, 25

Step-by-step 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.

Answer 2

Answer:

c

Step-by-step explanation:

just did it