Answer:
z = 3√13
Step-by-step explanation:
The length of z is the geometric mean of the segments of the longest side that share a common point with z. The shorter of those is 9; the longer one is 4+9 = 13. Then ...
z = √(9(13))
z = 3√13
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Additional comment
In like fashion, ...
- x = √(4(13)) = 2√13
- y = √(4·9) = 6.
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These relations come about because all of these right triangles are similar. That means their side lengths are proportional.
long side/hypotenuse = z/13 = 9/z ⇒ z = √(9·13)
short side/hypotenuse = x/13 = 4/x ⇒ x = √(4·13)
short side/long side = 4/y = y/9 ⇒ y = √(4·9)
