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

$\dfrac{h}{a}=\dfrac{b}{a}$

$h^2=ab$

$h=\sqrt{ab}$             [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

$\dfrac{n}{8}=\dfrac{4}{n}$

$n^2=4\times 8$

$n^2=32$

$n=\sqrt{32}$

Therefore, the measure of altitude is $n=\sqrt{32}$ units.