All of the triangles are similar, so the ratio of hypotenuse to long side is the same for all. Comparing the middle-size triangle to the largest, we have ...
... x/12 = 16/x
... x² = 192 . . . . . . . . . . . . . multiply by 12x; next take the square root
... x = √192 = 8√3 . . . . . . seems to match answer choice (a)
AnsweYou’ve seen two methods for finding the area of ΔABC—using coordinate algebra (by hand) and using geometry software. How are the two methods similar? How are they different? Why might coordinate algebra be important in making and using geometry software?