The diagonal, which is 18 inches is the hypotenuse of
the right triangle with legs x and y. Using the
Pythagorean theorem, we have the equation:


 

The area of the whole rectangle given as 150 square inches 
is the length x times the width y.  So we have the 
equation:



So we have the system:



Solve the second equation for y




Now we substitute  for  in the
equation:






Multiply through by  to clear of fractions:



Get 0 on the right by subtracting  from
both sides:



Get it in descending order:



That is choice (C).

Edwin