Question

What type of triangle has side lengths 45‾√ 4 5 , 145‾‾‾‾√ 145 , and 19 19 ?

Answer 1

It is not possible to form a triangle with the given side lengths.

Step-by-step explanation:

The given side lengths are 45√45, 145√145, and 19. To determine the type of triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's check:

1. 45√45 + 145√145 = 45√45 + 145√145 = 190√45 + 145√145 = 335√45 + 145√145 = 480√45 < 19
2. 45√45 + 19 = 45√45 + 19 = 64√45 < 145√145
3. 145√145 + 19 = 145√145 + 19 = 164√145 < 45√45

Based on the triangle inequality theorem, none of the conditions hold true, so it is impossible to form a triangle with the given side lengths. Therefore, there is no triangle that can be formed.

Learn more about triangle inequality theorem