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
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
Therefore, the required solutions for the given blanks are:
Blank 1: 72
Blank 2: 6
Blank 3: 2