Answer:
green box: 13
Step-by-step explanation:
The altitude from the right-angle vertex divides a right triangle into similar triangles. Corresponding sides of similar triangles are in proportion, so you have ...
... short side / long side = 4/y = y/9
Multiplying by 9y gives ...
... 36 = y²
... 6 = y . . . . taking the square root
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z is the hypotenuse of the right triangle with sides 6 and 9. So the value of z will be ...
... z² = 6² +9² . . . . . . Pythagorean theorem
... z = √(36 +81) = √(9·(4 + 9)) = 3√13
