Question

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 16 and 25. What is the length of the altitude?

Answer 1

if a and b are the two sides (base and alt.) of a right triangle, and 'c' is the hypotenuse (the side opposite to the right angle and also the longest side), then, according to the Pythagoras theorem,

\[\large \color{green}{a^2 + b^2 = c^2}\]

apply this.

Answer 2

so C = 25 and B = 16?

Answer 3

yeah. just plug in.

Answer 4

a = 20?

Answer 5

Theorem: If an altitude is drawn to the hypotenuse of a right triangle, either leg of the triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

16 is to a as a is to 25 where a is the length of the altitude to the hypotenuse.

16/a = a /25
a^2 = 16*25
a = 20 units