Answer:
[tex] x=\sqrt{10} [/tex]
[tex] y = \sqrt {14} [/tex]
[tex] z = \sqrt {35} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] x=\sqrt{2\times 5} [/tex]
[tex] x=\sqrt{10} [/tex]
By Pythagoras Theorem:
[tex] y^2 = x^2 + 2^2 [/tex]
[tex] y^2 = (\sqrt{10}) ^2 + 2^2 [/tex]
[tex] y^2 = 10 + 4 [/tex]
[tex] y^2 = 14 [/tex]
[tex] y = \sqrt {14} [/tex]
Again by Pythagoras Theorem:
[tex] z^2 = x^2 + 5^2 [/tex]
[tex] z^2 = (\sqrt{10}) ^2 + 5^2 [/tex]
[tex] z^2 = 10 + 25 [/tex]
[tex] z^2 = 35 [/tex]
[tex] z = \sqrt {35} [/tex]
