To find the compound inequality that describes all possible lengths of n, we need to consider the relationships between the given side lengths.
Given that the sides of the sandbox are 9ft, 6ft, and n ft, we know that the sum of the two shorter sides must be greater than the longest side according to the triangle inequality theorem. In other words, the sum of any two sides of a triangle must be greater than the length of the remaining side.
So, for this sandbox, we can write the compound inequality as follows:
"6ft + 9ft > n and n + 6ft > 9ft and n + 9ft > 6ft"
This compound inequality represents the necessary conditions for the lengths of the sandbox sides. The first part, 6ft + 9ft > n, ensures that the sum of the two shorter sides (6ft and 9ft) is greater than the longest side (n). The second and third parts, n + 6ft > 9ft and n + 9ft > 6ft, ensure the same for the other two pairs of side lengths.
By satisfying this compound inequality, any value of n that satisfies these conditions will be a possible length for the third side of the sandbox.
The lengths of the sides of a sandbox are 9ft, 6ft and n ft. Write a compound inequality that describes all possible lengths of n.
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