Answer: The answer is x = 21, y = 5√21 and z = 2√21.
Step-by-step explanation: As given in the question and shown in the attached figure, ΔABC, ΔABD and ΔACD are all right-angled triangles. Here, AB = 10 and BD = 4, We need to find the values of 'x', 'y' and 'z'.
From the right-angled triangle ΔABD, we have after using Pythagoras theorem that
[tex]AB^2=BD^2+AD^2\\\\\Rightarrow 10^2=4^2+z^2\\\\\Rightarrow 100=16+z^2\\\\\Rightarrow z^2=84\\\\\Rightarrow z=2\sqrt{21}.[/tex]
Again, from the right-angled triangles ΔABC and ΔACD, we have
[tex]AB^2+BC^2=AC^2\\\\\Rightarrow 100+y^2=(4+x)^2\\\\\Rightarrow 100+y^2=x^2+8x+16,[/tex]
and
[tex]AC^2=AD^2+CD^2\\\\\Rightarrow y^2=z^2+x^2\\\\\Rightarrow y^2=84+x^2.[/tex]
Subtracting the above equation from the previous one, we have
[tex]100=8x+16-84\\\\\Rightarrow 8x=168\\\\\Rightarrow x=21.[/tex]
And finally,
[tex]y=\sqrt{84+441}=\sqrt{525}=5\sqrt{21}.[/tex]
Thus, x = 21, y = 5√21 and z = 2√21.
