The following geometric object was first investigated by the Greek mathematician Theodorus. Every triangle shown below is a right triangle.What isx?Hint: It will help if you first findc1, thenc2,c3,andc4before findingx.

Answer  :
We have our figure , As :


x here is length of hypotenuse.

To find value of x , we follow these steps 
Step 1 - We apply Pythagoras theorem in triangle 1 , and get

c₁²  = 1² + 1² 

c₁² = 2

c₁  = $\sqrt{2}$ 

Step 2 - ​We apply Pythagoras theorem in triangle 2 , and get
Now we have base  c₁  = $\sqrt{2}$   , So

c₂² = 1² + $\sqrt{2}$ ​² 

c₂² = 3

c₂  = $\sqrt{3}$

Step 3 - ​We apply Pythagoras theorem in triangle 3 , and get
Now we have base  c₂  = $\sqrt{3}$   , So

c₃² = 1² + $\sqrt{3}$ ² 

c₃² = 4

c₃  = 2


Step 4 - We apply Pythagoras theorem in triangle 4 , and get
Now we have base  c₃  = 2   , So

c₄² = 1² + 2 ² 

c₄² = 5

c₄  = $\sqrt{5}$

Step 5 - We apply Pythagoras theorem in triangle 5 , and get
Now we have base  c₄  = $\sqrt{5}$   , So

x²  = 1² + $\sqrt{5}$² 

x² = 6

x  = $\sqrt{6}$                                          ( Ans )