Question

Need help with a math question

Answer 1

Answer:

$z =3\sqrt{13}$

Step-by-step explanation:

In the figure you can identify up to 3 straight triangles.

To solve the problem, write the Pythagorean theorem for each triangle.

Triangle 1

$13^2 = z^2 + x^2$

Triangle 2

$z^2 = y^2 + 9^2$

Triangle 3

$x^2 = y^2 + 4^2$

Now substitute equation 2 and equation 3 in equation 1 and solve for y.

$13^2 = y^2 + 9^2 + y^2 + 4^2$

$13^2 = 2y^2 + 9^2 + 4^2$

$169 = 2y^2 + 81 + 16$

$2y^2 =72$

$y^2 =36$

$y =6$

substitute the value of y in the second equation and solve for z

$z^2 = 6^2 + 9^2$

$z^2 = 36 + 81$

$z^2 = 117$

$z = \sqrt{117}$

$z =3\sqrt{13}$