Hello from MrBillDoesMath!
Answer:
x =2, y= 3, z = 1
Discussion:
Applying the Pythagorean thereon to the leftmost triangle gives:
y^2 + (sqrt(3))^2 = (sqrt(12)
) ^2 =>
y^2 + 3 = 12 => subtract 3 from both sides
y^2 = 12 - 3 = 9 => take square root of both sides
y = 3
In the full triangle, based on similar triangles, we have
(y + z) / (sqrt(12)) = sqrt(12)/y => multiply both sides by sqrt(12)
(y + z) = (sqrt(12)^2 /y => multiply both sides by y
y(y+z) = 12 => y = 3. Substitute.
3 (3 + z) = 12 => divide both sides by 4
(3+z) = 12/3 =4 => subtract 3 from both sides
z = 4 -3 = 1
Finally, using Pythagoras in the small rightmost triangle gives
x^2 = ((sqrt(3))^2 + z^2 => simplify
x^2 = 3 + z^2 => but z = 1 from above. Substitute
x^2 = 3 + 1^2 = 4 => take square roots of both sides
x = sqrt(4) = 2
Conclusion: x =2, y= 3, z = 1
Thank you,
MrB
