I need help on geometry math problem?
Okay so there is a triangle. It looks like this:
http://jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/Brooks/6690stuff/Righttriangle/Image33.gif
On line AC, there is the measurement: 15
On line CD, there is the measurement: x
On line DB, there is the measurement: 16
On line AD, there is the measurement: y
On line AB, there is the measurement: z
(It helps if you draw it out to get a clear picture of what it looks like.)
I need to find the lengths of x, y, and z in simplest radical form using the geometric mean formula which is this:
x^2=sqrt(ab)
(x to the second power equals the square root of a times b)
I have tried many times and can not seem to get it. Some one please help me! Show me the steps to do it too please :]
Thank you so much!
I will give points to whoever answers it the best :]
AD/DB = CD/AD from the fact that the altitude AD is the geometric mean between the two sections of the hypotenuse.
y/16 = x/y which gives y^2 = 16x from cross multiplication.
from the Pythagorean theorem, on the small triangle CDA, you get
x^2 + y^2 = 15^2 substitute from the above equation 16x for y^2 and get
x^2 + 16x = 225
x^2 + 16x – 225 = 0
(x-9)(x+25) = 0
since x must be positive, x = 9
Since from above y^2 = 16x, y^2 = 16(9),
y = 12
also corresponding parts of similar triangles, you get
DB/AB = AB/CB which is
16/z = z/(x+16) substitute x =9,
16/z = z/25 cross multiply
z^2 = 16(25)
z = 20
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