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Triangles
6
In triangle
ABC, the length of side
AB is 10 inches and the length of side
BC is 17 inches. Which of the following could be the length of side
AC ?
A. 5 inches
B. 29 inches

Triangles $\newline$ $6$ $\newline$ In triangle $A B C$ , the length of side $A B$ is $10$ inches and the length of side $B C$ is $17$ inches. Which of the following could be the length of side $A C$ ? $\newline$ A. $5$ inches $\newline$ B. $29$ inches

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Find missing angles in special triangles

Full solution

Q. Triangles

\newline

6

\newline

In triangle

A B C

, the length of side

A B

is

10

inches and the length of side

B C

is

17

inches. Which of the following could be the length of side

A C

?

\newline

A.

5

inches

\newline

B.

29

inches

Introduction: To determine the possible length of side AC, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's denote the length of side AC as $x$ .
Check Option A: First, we check if option A ( $5$ inches) could be the length of side $AC$ . According to the Triangle Inequality Theorem, we must have: $\newline$ $AB + AC > BC$ $\newline$ $10 + 5 > 17$ $\newline$ $15 > 17$ $\newline$ This is not true, so $5$ inches cannot be the length of side $AC$ .
Check Option B: Next, we check if option B ( $29$ inches) could be the length of side $AC$ . Again, using the Triangle Inequality Theorem: $\newline$ $AB + AC > BC$ $\newline$ $10 + 29 > 17$ $\newline$ $39 > 17$ $\newline$ This is true. However, we must also check the other two inequalities to ensure that $29$ inches is a valid length for $AC$ : $\newline$ $AC + BC > AB$ $\newline$ $29 + 17 > 10$ $\newline$ $46 > 10$ $\newline$ This is true.
Final Check: Finally, we check the last inequality: $\newline$ $AB + BC > AC$ $\newline$ $10 + 17 > 29$ $\newline$ $27 > 29$ $\newline$ This is not true, so $29$ inches cannot be the length of side $AC$ either.

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