Question

Altitudes in Right Triangles Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 1 of 51 of 5 Items Question Use the image to answer the question. Given is the right triangle MNP with altitude MO . Find the value of x. Provide an exact answer in improper fraction form. (1 point) x= Remaining Attempts : 3 Skip to navigation page 14 of 15

Answer 1

To solve for \( x \) in the right triangle \( MNP \) with altitude \( MO \), we can use the relationship between the segments created by the altitude drawn from the right angle to the hypotenuse of the triangle.

In a right triangle, if you drop an altitude from the right angle to the hypotenuse, it divides the triangle into two smaller right triangles that are similar to each other and to the original triangle.

Using the geometric mean relationship, we have: \[ MO^2 = MP \cdot ON \] This gives us a way to express the altitude in terms of the segments of the hypotenuse that it creates.

Since I do not have the specific lengths from your question, I'll give you the general method:

1. Identify and clearly label all the known lengths of the triangle, including \( MP \), \( ON \), and the lengths of the sides of the triangle.
2. Substitute the known values into the equation above or another relevant relationship (like Pythagorean theorem or other similarity relationships).

If you can provide the lengths or values associated with triangle \( MNP \) (like \( MP \) and \( ON \)), I can help you solve for \( x \) more specifically. Otherwise, applying the geometric mean theorem step will yield your value for \( x \).