Given:
A figure of a right angle.
To find:
The value of x.
Solution:
We know that the measure of the altitude on the hypotenuse of a right right triangle is the geometric mean of the segments of the hypotenuse.
If the altitude "h", divides the hypotenuse in two segments "a" and "b", then
[tex]h=\sqrt{ab}[/tex]
In the given figure, the measure of the altitude is x and it divides the hypotenuse in two segments 3 units and 24 units.
Using the above theorem, we get
[tex]x=\sqrt{3\times 24}[/tex]
[tex]x=\sqrt{72}[/tex]
[tex]x=6\sqrt{2}[/tex]
Therefore, the required solutions for the given blanks are:
Blank 1: 72
Blank 2: 6
Blank 3: 2
