Atriangle has one side length of 12 inches and another of 8 inches. describe all possible lengths of the third side. show and explain your reasoning.

The third side must be smaller than 20 inches and greater than 4 inches

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

Use this rule in your case. So, if a=12 and b=8, then

Hence, you get

From these inequalities, you can state that

So, c must be smaller than 20 inches and greater than 4 inches.

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

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step-by-step explanation: