Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches.
What is the greatest possible whole-number length of the unknown side?

The greatest possible whole-number length is 7 inches

Step-by-step explanation:

Before we go on to answer this question, we primarily need to understand what is meant by the term obtuse triangle. An obstuse triangle can be defined as a triangle having an obtuse angle and two acute angles.

When we talk about angles, we mean angles greater than 90 but less than 180 while acute are angles less than 90

By definition, for an obtuse triangle, the following relation hold strictly.

C^2 > a^2 + b^2

What does this mean? This is trying to tell us that the square of the longest side is greater than the sum of the squares of the two other sides. It was specified from the question that the longest side is 14 inches, this automatically means that c = 14 inches

14^2 > 12^2 + b^2

196 > 144 + b^2

196-144 > b^2

52 > b^2

7.2 > b

Let’s round this off to the nearest whole number to give us 7 inches

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step-by-step explanation:

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