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.
To write the compound inequality that describes all possible lengths of n, we need to consider the conditions that must be met for n to be a valid length of the third side of the sandbox.
According to the triangle inequality theorem, in a triangle with sides a, b, and c, the sum of the lengths of any two sides must be greater than the length of the remaining side.
In this case, we have sides of lengths 9ft, 6ft, and n ft. Therefore, the compound inequality that describes all possible lengths of n can be written as:
9ft + 6ft > n and 9ft + n > 6ft and 6ft + n > 9ft