Answer:
3√10
Given:
A right triangle in which an altitude is drawn from the right angle vertex
To find: value of X
We have leg rule in similarity in right triangle as:
[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ [/tex]
Plugging the given values,
[tex] \frac{z}{3} = \frac{3 + 27}{z} \\ z \times z = 3(3 + 27) \: \: (cross \: multiplication) \\ {z}^{2} = 9 + 81 \\ {z}^{2} = 90 \\ z = \sqrt{90} \\ z = 3 \sqrt{10} [/tex]
Hope this helps...
Good luck on your assignment..
