1972 AHSME Problems/Problem 27
If the area of is square units and the geometric mean (mean proportional) between sides and is inches, then is equal to
Draw Diagram later
We can let and . We can also say that the area of a triangle is , which we know, is . We also know that the geometric mean of and is 12, so .
Squaring both sides gives us that . We can substitute this value into the equation we had earlier. This gives us
-edited for readability