Question

How does this work??

Answer 1

Hello from MrBillDoesMath!

Answer:

See below

Discussion:

This picture appears to be an application of the Pythagorean theorem. That is, the sum of the squares of the legs equals  the square of he hypotenuse. Let's check this out.

Does

(leg1)^2 + (leg2)^2   = (hypotenuse)^2

5^2       + 5^2          = (5 sqrt(2)) ^ 2   ?         => number from diagram

25          + 25           =  5 * 5 * (sqrt(2) ) ^ 2   =>   as (sqrt(2)) ^ 2 = 2

25 + 25 = 5*5*2 = 50 =>

50 = 50.      

Indeed.

Note: this is an  isosceles triangle as the base angles equal 45 degrees.  It illustrates that in an isosceles triangle the length of the hypotenuse is the length of either leg times the sqrt(2)

Thank you,

MrB