Question

Determine the possible side lengths of the third side of a triangle with known side lengths of 5 and 8.

Question 3 options:

A)

–5 < c < –8

B)

–3 < c < –13

C)

3 < c < 13

D)

5 < c < 8

Answer 1

Answer: 9.43398113206

Step-by-step explanation:

A^2 + B^2 = C^2

5^2 + 8^2 = √89

= 9.43398113206

Answer 2

Answer: 3 < c < 13 (choice C or third answer choice)

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Step-by-step explanation:

Consider a triangle with sides: a,b,c

Furthermore, we'll have a = 5 and b = 8 as the two known sides.

Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:

b-a < c < b+a

where b ≥ a must be the case.

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Let's plug in those a & b values to determine the range for c.

b-a < c < b+a

8-5 < c < 8+5

3 < c < 13

This points us to Choice C as the final answer.