Hi all, I have an answer which is puzzeling me
from the answer page it reads;
if L is the length of the shorter edge, by pythag` theorem, 2L^2 =a^2, so L^2=1/2a^2
Hence the shorter edge L, has length a/sqrt 2
if it helps the picture is a right angled triangle with a hyp` of length given as a, and the two shorter lenghts given as L
what I can`t get is why the shorter edge L, has length a/sqrt 2
Dave
Sorry, you did not specify the last claim of the proof that you understand. This must mean that you don't understand why L^2 + L^2 = a^2. This is an instance of the Pythagoras theorem because we have a right-angled triangle with two sides of length L and the hypotenuse of length a.
So, we have 2L^2 = a^2. Divide both sides by 2. Now, take the square root of both sides.
I am just repeating the proof you gave. I am still curious to know which exactly part of it you don't understand.
Look, is it too hard for you to say: "This equality I understand, but how this one follows from it I don't understand."
We have the following theorems about square root:
(1) If , then .
(2) If and , then .
So, we have the following derivation.
1. From the Pythagoras theorem, . Divide both sides by 2.
2. . Take square root of both sides.
3. . Apply (2)
4. . Apply (1)
5. .
Could you say which of the facts (1), (2) and steps 1-5 were not clear to you?