Question

Using Pythagorean inequalities, determine which of the following sets of values can represent the lengths of the sides of a right triangle.

Answer 1

The identities are:
If c^2 > a^2 + b^2 the triangle is an obtuse triangle
If c^2 < a^2 + b^2 then triangle is an acute triangle
If c^2 = a^2 + b^2 the triangle is a right triangle
The longest length always goes in for C.
A.  6^2 <,>,= 4^2 + 5^2
36 <,>,= 16 + 25
36 ____41  36< 41 acute

B.  19^2 <,>,= 5^2 + 13^2
361 <,>,= 25 + 169
361 ____194  361 > 194 obtuse

C.  25^2 <,>,= 12^2 + 14^2
625 <,>,= 144 + 196
625 <,>,= 340
625  ___ 340  625 > 340 obtuse

D.  75^2 <,>,= 21^2 + 72^2
5625 <,>,= 441 + 5184
5625 <,>,= 5625
5625 = 5625 right triangle
LETTER D