Find the value of x, y, and z reduced to the simplest radical form. :confused: Please explain! Thank you in advance!

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- May 5th 2007, 12:52 PMIHATECHONGAStriangle
Find the value of x, y, and z reduced to the simplest radical form. :confused: Please explain! Thank you in advance!

- May 5th 2007, 12:54 PMIHATECHONGASDiagram
Ooops...forgot diagram...Here it is!

- May 5th 2007, 01:06 PMJhevon
ok, because i ws wondering what x, y, and z are you talking about?

so by Pythagoras' theorem:

x = sqrt(y^2 - 4^2) and also x = sqrt(z^2 - 2^2)

=> sqrt(y^2 - 4^2) = sqrt(z^2 - 2^2)

=> y^2 - 16 = z^2 - 4

=> y^2 - z^2 = 12 ..................(1)

by Pythagoras' theorem:

y = sqrt(6^2 - z^2) and also y = sqrt(x^2 + 4^2)

=> sqrt(6^2 - z^2) = sqrt(x^2 + 4^2)

=> 36 - z^2 = x^2 + 16

=> x^2 + z^2 = 20 ...................(2)

by Pythagoras' theorem:

z = sqrt(6^2 - y^2) and also z = sqrt(x^2 + 2^2)

=> sqrt(6^2 - y^2) = sqrt(x^2 + 2^2)

=> 36 - y^2 = x^2 + 4

=> x^2 + y^2 = 32 ....................(3)

So we have the system:

y^2 - z^2 = 12 ..................(1)

x^2 + z^2 = 20 ..................(2)

x^2 + y^2 = 32 ..................(3)

solving this system should give you your values

can you take it from here?