Given:
The figure of a right triangle.
To find:
The measure of x.
Solution:
According to the altitude on hypotenuse theorem, the length of the altitude is the geometric mean of segments of the hypotenuse.
Let "h" be the height of the altitude and it divides the hypotenuse if two pieces of lengths "a" and "b", then
[tex]h=\sqrt{ab}[/tex]
In the given figure, 14 is the height of the altitude and it divides the hypotenuse if two pieces of lengths 24 and x. So, by using the altitude on hypotenuse theorem, we get
[tex]14=\sqrt{24x}[/tex]
Taking square on both sides.
[tex]196=24x[/tex]
[tex]\dfrac{196}{24}=x[/tex]
[tex]\dfrac{49}{6}=x[/tex]
Therefore, the value of x is [tex]\dfrac{49}{6}[/tex] units and its approximate value is 8.167 units.
