A right triangle has a segment from the right angle that meets the hypotenuse at a right angle at point p. Point p splits the hypotenuse into two segments whose lengths are 16 units and 4 units. Find the distance from the perpendicular line to the right angle.

Question

A right triangle has a segment from the right angle that meets the hypotenuse at a right angle at point p. Point p splits the hypotenuse into two segments whose lengths are 16 units and 4 units. Find the distance from the perpendicular line to the right angle.

Answer 1

Let's denote the length of the perpendicular line from point P to the right angle as x.

Using the properties of similar triangles, we can set up the following ratio:

x/4 = (x + 16)/16

Cross-multiplying, we have:

16x = 4(x + 16)

Simplifying the equation, we have:

16x = 4x + 64

12x = 64

Dividing both sides by 12, we find:

x = 64/12

x = 16/3

Therefore, the distance from the perpendicular line to the right angle is 16/3 units.