Question

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3.
What is the length of line segment LJ?

9 units
12 units
15 units

Answer 1

When an altitude is drawn from the right angle to the hypotenuse, the altitude squared equals the product of the two segments of the hypotenuse: KM^2 = MJ · ML.

Given KM = 6 and MJ = 3:
36 = 3 · ML → ML = 12.

Then LJ = MJ + ML = 3 + 12 = 15 units.

Answer: 15 units.