Question

What is the measure of n?

Answer 1

Given:

A figure of a right triangle whose altitude divides the opposite in two segments of 8 and 4 units.

The measure of the altitude is n.

To find:

The value of n.

Solution:

According to the altitude on hypotenuse theorem, the altitude on the hypotenuse of a right triangle is geometric mean of two segments of the hypotenuse.

Let the altitude h divides the hypotenuse in two parts with measure a and b, then

`(h)/(a)=(b)/(a)`

`h^2=ab`

`h=√(ab)` [Because side length cannot be negative]

In the given figure, the altitude is n and it divides the hypotenuse in two segments of 8 units and 4 units.

Using altitude on hypotenuse theorem, we get

`(n)/(8)=(4)/(n)`

`n^2=4* 8`

`n^2=32`

`n=√(32)`

Therefore, the measure of altitude is
`n=√(32)` units.