Question

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown/ What is the greatest possible whole-number length of the unknown side?
8 inches
9 inches
12 inches
13 inches

Answer 1

Answer:

12in

Step-by-step explanation:

Answer 2

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.

What is the triangle inequality theorem?

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

 $(a+b) > c\\(b+c) > a\\(c+a) > b$

Given the length of the two sides of the triangle, therefore, we can write the inequalities,

8 + 5 > x  ⇒   13 > x

8 + x > 5  ⇒  x > - 3

5 + x > 8  ⇒  x > 3

Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.

Hence, the correct option is C.

Learn more about the Triangle Inequality Theorem:

brainly.com/question/342881

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