Question

A right triangle is drawn on a coordinate plane with a line drawn from the right angle that isperpendicular to the hypotenuse. The hypotenuse consists of a short line segment measuring 2 unitsand a long line segment measuring 30 units. Using the geometric mean, what is the distance of theshort leg of the original triangle?
(1 point)
5.3 units
60 units
28 units
8 units

Answer 1

Let the hypotenuse be c = 2 + 30 = 32, and let the short leg be a adjacent to the short hypotenuse segment d = 2. By the geometric-mean property for right triangles, a^2 = c·d = 32·2 = 64, so a = 8 units.

Answer: 8 units.