Multiple choice

The perpendicular dropped from a vertex of a right-angled triangle upon the hypotenuse divides it into two segments of lengths 9 units and 16 units, respectively. What is the length of the perpendicular?

  1. 6 units

  2. 8 units

  3. 10 units

  4. 12 units
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a right-angled triangle, the altitude h to the hypotenuse divides it into segments p and q. The geometric mean theorem states h^2 = p * q. Here, h^2 = 9 * 16 = 144, so h = 12.

AI explanation

Using the geometric mean theorem (altitude rule) for right triangles, the length of the perpendicular to the hypotenuse is the square root of the product of the two segments it creates. The segments are 9 and 16, so the perpendicular length is sqrt(9 * 16) = sqrt(144) = 12. The result is 12 units.

Keep practicing — related questions