Question

Triangle side length rules ​

Answer 1

Answer:

5.5<x<10.5

Step-by-step explanation:

given three side lengths, they can form a triangle if and only if the sum of any two lengths is larger than the third side. Given the side lengths for the triangle in the picture,

x + 2.5 > 8

2.5 + 8 > x

8 + x > 2.5

since the last inequality is automatically true no matter whatever length x is, we will disregard it.

now use algebraic manipulation to isolate x in each inequality

x + 2.5> 8

x + 2.5 -2.5 > 8 - 2.5

5.5<x

2.5 + 8 > x

x<10.5

by combining the two inequalities we have, we know that

5.5<x<10.5