Question

A right triangle is drawn on a coordinate plane with a line from the right angle that is perpendicular to the hypotenuse. The hypotenuse consists of a short line segment measuring 2 units and a long line segment measuring 30 units.

Using the geometric mean, what is the distance of the short leg of the original triangle?

A. 5.3 units
B. 28 units
C. 60 units
D. 8 units

Answer 1

Let the hypotenuse be c = 2 + 30 = 32, and let the short segment adjacent to the short leg be 2. In a right triangle with altitude to the hypotenuse, each leg is the geometric mean of the hypotenuse and the adjacent hypotenuse segment:

short leg = sqrt(c * short segment) = sqrt(32 * 2) = sqrt(64) = 8.

Answer: D.