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

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.

anonymous · Answer

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directrix · Answer

I assume that the task is to find the length of XZ.

YA = 8 because of the Pythagorean theorem or if you know about the Pythagorean Triples, 6, 8, 10 is a 2-multiple of (3,4,5).

Next find AZ.

8/6 = 6/AZ

This is because if an altitude is drawn to the hypotenuse of a right triangle,  then the altitude is the geometric mean of the lengths of the segments of the hypotenuse.

So, 8/6 = 6/AZ

and AZ = 9/2

XZ = XA + AZ = 8 + 9/2 = 25/2 = 12.5