The figure below shows a bamboo support made to hold bean plants. What is the distance between the points X and Z of the support? Show all the steps you used to find your answer.

Question

anonymous · Answer

attachment

mertsj · Answer

Each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

anonymous · Answer

Me=confused... Haha .

mertsj · Answer

$$\frac{8}{10}=\frac{10}{XZ}$$

anonymous · Answer

Oh wait.. I think I know how to do it now.. Thank you :)

anonymous · Answer

Okay, I was wrong . I still don't get it :/

directrix · Answer

Theorem: If an altitude is drawn to the hypotenuse of a right triangle, either leg of the triangle is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg. 

8 is to 10 as 10 is to XZ

Note that XZ = 8 + AZ

8/10 = 10/(8 + AZ)

4/5 = 10/(8 + AZ)

4( 8 + AZ) = 50

32 + 4 AZ = 50

4 AZ = 50 - 32

4 AZ = 18

AZ = 18/4 = 9/2 = 4.5

XZ = 8 + AZ

XZ = 8 + 4.5 = 12.5  ---> Answer