Question

Solve for x in the partial spiral below.

Answer 1

After further application of Pythagoras Theorem on all triangles of the spiral, we get the hypotenuses as in order: root 2, root 3, 2, root 5
Thus, the final hypotenuse, i.e., x, has the value of root 5

Answer 2

Answer:

$x = \sqrt 5$

Step-by-step explanation:

On solving by Pythagoras theorem:

(Going in counterclockwise direction)

For bottom most triangle :

Length of Hypotenuse $= \sqrt {1^2 +1^2} =\sqrt {1+1}=\sqrt 2$

The for second triangle :

Length of Hypotenuse $= \sqrt {(\sqrt 2) ^2 +1^2} =\sqrt {2+1}=\sqrt 3$

The for third triangle :

Length of Hypotenuse $= \sqrt {(\sqrt 3) ^2 +1^2} =\sqrt {3+1}=\sqrt 4 = 2$

The for fourth triangle :

x $= \sqrt {(2) ^2 +1^2} =\sqrt {4+1}=\sqrt 5$