Question

If the longest side of triangle WVU measures 17 inches and another side measures 9 inches, which of the following is the measure for the third side?

A. 6 in
B. 8 in
C. 9 in
D. 7 in

Answer 1

Option C. 9 in

Explanation:

The question is

What can be the length of the third side?

we know that

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let

x ----> the length of the third side

Applying the Triangle Inequality Theorem

1) x+9 > 17

x > 17-9

x > 8 in

2) 9+17 > x

26 > x

Rewrite

x < 26 in

so

The solution for the third side is the interval ----> (8,26)

All real numbers greater than 8 inches and less than 26 inches

therefore

The measure of the third side can be 9 in