Use the Pythagorean theorem (several times) to find the exact (do not approximate) length of segment AB in the adjacent figure.

Question

 

A _1_____1__

   \      |       /  |

     \    |    /     |    

       \  |  /       |  1

         \| /____ |

     B             1

Answer 1

Based on the measurements of the diagram, the entire triangle is an isosceles triangle.  So we only have to use the Pythagorean theorem once.

 

AB = √(1 + 1)

AB = √2

Answer 2

Nice effort to make a drawing. 

I make AB out to be √2.

I don't see why the Pythagorean Theorem would be required more than once.

Answer 3

By the symmetry of the figure, the length of AB is

 

√(1² + 1²) = √2