Question

Use the converse of the Pythagorean theorem to determine if the three given side lengths form a right triangle. 7 cm, 12 cm, 14 cm

Answer 1

The Pythagorean Theorem states right triangles produce the following relationship between the sides of the triangle:  a² + b² = c² where a and b represent the legs of the right triangle and c represents the hypotenuse of the right triangle... 

The converse of the theorem states that if the relationship of the sides is true, then you must have a right triangle.. 

Lets's substitute the side lengths into the theorem and see if we have a right triangle:   

7² + 12² = 14²  or 49 + 144 = 196
193 ≠ 196 and therefore the three sides given do not represent the sides of a right triangle. 

Answer 2

Using the Pythagorean Theorem a^2 + b^2 = c^2:-

7^2 + 12^2 = 142

49 + 144 = 196

193 = 196