Question

How do you find points X, Y, and Z? Thank you and I will mark as Brainliest and 15 points!

Answer 1

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

$AB^2=BD^2+AD^2\\\\\Rightarrow 10^2=4^2+z^2\\\\\Rightarrow 100=16+z^2\\\\\Rightarrow z^2=84\\\\\Rightarrow z=2\sqrt{21}.$

Again, from the right-angled triangles ΔABC and ΔACD, we have

$AB^2+BC^2=AC^2\\\\\Rightarrow 100+y^2=(4+x)^2\\\\\Rightarrow 100+y^2=x^2+8x+16,$

and

$AC^2=AD^2+CD^2\\\\\Rightarrow y^2=z^2+x^2\\\\\Rightarrow y^2=84+x^2.$

Subtracting the above equation from the previous one, we have

$100=8x+16-84\\\\\Rightarrow 8x=168\\\\\Rightarrow x=21.$

And finally,

$y=\sqrt{84+441}=\sqrt{525}=5\sqrt{21}.$

Thus, x = 21, y = 5√21  and  z = 2√21.