Well I don't know where inequalities would come in but the third length would be solved as follows.
a^2+b^2=c^2
10^2+18^2=424

Answer;

I hope this is correct, its what I would do if I had this equation.
Answer:
B. Similar - AA
Step-by-step explanation:
Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.
Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.
Answer:
The first four terms in the sequence 57, 50, 43, and 36
Step-by-step explanation:
Put the numbers in place of x (or n in this case).
You subtract that number you put in place of n by 1.
You then distribute the difference of n and 1.
You then subtract the distributed number by 57
Answer:
The discriminant D=0
Step-by-step explanation:
For the duadratic polynomial
the discriminant is

In your case, for the polynomial 
The height of the doorway is 252 inches