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Jasmine is making a triangular garden. Two sides of the garden measure 6 feet by 11 feet. What is the range of the possible lengths, in feet, for the third side, x, of the garden?

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By using the triangle inequality, we conclude that the possible length of the third side is 5ft < x < 17ft.

What is the range of the possible lengths for the third side?

For a triangle of sides A, B, and C, the triangle inequality says that the sum of any two sides is larger than the other side, so we have:

A + B > C

A + C > B

C + B > A

In this case, two sides measure 6ft and 11ft, and the missing side measures x.

Then we will have:

6ft + 11ft > x

x + 6ft > 11ft

x + 11ft > 6ft

From the first inequality we get the upper bound:

6ft +11 ft > x

17ft > x.

Now, using the second we get:

x + 6ft > 11ft

x > 11ft - 6ft

x > 5ft

(We don't use the last inequality because it will say that x must be larger than a negative number, and the above inequality is more restrictive than that).

Then, if we use the two inequalities that we got we have:

5ft < x < 17ft

The possible length of the third side is 5ft < x < 17ft.

If you want to learn more about triangles, you can read:

https://brainly.com/question/1675117

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