The lengths of the missing sides of the triangle are:
c = 9
d = 7
e = 7.94
How to use the Altitude on Hypotenuse Theorem?
The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse. This is known as the Altitude-on-Hypotenuse Theorem.
Using the formula for Altitude-on-Hypotenuse Theorem we can say that:
12 = √(16c)
Square both sides to get:
144 = 16c
c = 9
Thus:
d = 16 - 9
d = 7
Using the formula for Altitude-on-Hypotenuse Theorem we can say that:
e = √(cd)
e = √(9 * 7)
e = √63
e = 7.94