Geometric Mean with Right Triangles

In a right triangle, _____ to the hypotenuse creates two similar right triangles.

In a right triangle, if the length of the altitude drawn to the hypotenuse is 6 units and the length of the segment of the hypotenuse adjacent to the altitude is 9 units, what is the length of the other segment of the hypotenuse?

• 4 units

• 12 units

• 3 units

• 6 units

What is the geometric mean of the lengths of the segments of the hypotenuse created by the altitude in a right triangle, if one segment is 4 units and the other is 9 units?

• 6 units

• 6.5 units

• 7 units

• 5.5 units

If the length of the altitude to the hypotenuse of a right triangle is equal to the geometric mean of the lengths of the segments of the hypotenuse it divides, and one segment is 8 units, what is the length of the altitude?

• 8 units

• 4 units

• 6 units

• 10 units

In a right triangle, the altitude to the hypotenuse divides the hypotenuse into segments of lengths 5 units and 12 units. What is the length of the altitude?

• 6 units

• 7.2 units

• 8 units

• 9.6 units

How does the altitude to the hypotenuse of a right triangle relate to the two segments of the hypotenuse it creates?

• It is equal to the sum of the lengths of the two segments.

• It is the geometric mean between the lengths of the two segments.

• It is equal to the difference between the lengths of the two segments.

• It has no specific relationship to the lengths of the two segments.

Given a right triangle with a hypotenuse of 13 units and one leg of 5 units, what is the length of the altitude drawn to the hypotenuse?

• 12 units

• 5 units

• 6 units

• 60/13 units

In a right triangle, if the altitude to the hypotenuse is 8 units and one segment of the hypotenuse is twice the length of the other, what is the length of the shorter segment?

• 4 units

• 8 units

• 5.33 units

• 6.4 units

What is the relationship between the lengths of the legs of a right triangle and the altitude drawn to the hypotenuse?

• The altitude is the arithmetic mean of the lengths of the legs.

• The altitude is the geometric mean of the lengths of the legs.

• The altitude is the harmonic mean of the lengths of the legs.

• There is no direct relationship between the lengths of the legs and the altitude.

If the lengths of the segments of the hypotenuse created by the altitude in a right triangle are 7 units and 24 units, what is the length of the altitude?

• 12 units

• 14 units

• 16 units

• 12.8 units