Question

Show your work or describe your method to verify your answer

The measures of two sides of a triangle are 8 feet and 12 feet. Use values to fill in the blanks to create a true statement about the length of the third side of the triangle.

The third side of the triangle must be a larger value of ____ but smaller than ____.

Answer 1

Explanation:

To find the possible range for the length of the third side of the triangle, we can use the triangle inequality theorem. According to this theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, we have two sides with lengths of 8 feet and 12 feet. Let's call the length of the third side "x". Using the triangle inequality theorem, we can write the following inequality:

8 + 12 > x

Simplifying the inequality, we have:

20 > x

So, the length of the third side must be greater than 20 feet.

However, we also need to consider that the length of the third side cannot be greater than the sum of the two given sides. In this case, the sum of the two given sides is 8 + 12 = 20 feet. Therefore, the length of the third side must be smaller than 20 feet.

To summarize, the third side of the triangle must be a larger value than 20 feet, but smaller than 20 feet.

In conclusion, the possible range for the length of the third side of the triangle is greater than 20 feet and smaller than 20 feet.