2.There is this theorem stating that the length of the altitude drawn to the hypotenuse of a right triangle is the geometric mean between the segments that the hypotenuse is divided into. In numerical form it would look like this:
6/altitude = altitude/x-6
We can solve the length of the altitude by using Pythagorean Theorem. The altitude creates two triangles within the large triangle. We will be using 6 and 10 to find the altitude. Fortunately, instead of squaring the sides we can simply use the common triple: 3,4,5 to deduce that the length of the altitude is 8.
Now that we have the value for the altitude we can substitute it into the equation above.
6/8=8/x-6
Cross multiply
64 = 6x - 36
Add 36 to both sides
100 = 6x
50=3x
50/3=x
13. There is another theorem that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle. In numerical form it would look like this:
20/x = 12/6
cross multiply
12x = 120
x=10
