Question

Need help with a math question

Answer 1

`z =3√(13)`

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 = √(117)`

`z =3√(13)`