Question

Given that the diagonal of a square is (1-5*square root 2)/(4-4*square root2), calculate p^2, where p is the perimeter of this square. Given your answer in the form a+b*square root 2 where a and b are real numbers.

I arrive at a ans of (51-10*square root 2)/(6-4*square root 2) but I am not sure about my answer.

Answer 1

given that a square is just a 45-45-90 with sides of 1-1-sqrt(2)

this seems to be a question related to that little phenomenon

Answer 2

a side is p/4

Answer 3

first of all...we know that P = 4s where s = side
and the diagonal = s sqrt 2

so the relationship between perimeter and diagonal is...

d = (p sqrt 2)/2

...that's a good palce to start :D

Answer 4

\[\frac{1-5\sqrt{2}}{4-4\sqrt{2}}=\sqrt{2}\]
\[x=1\]

Answer 5

so id say x; which is my side is:\[\dfrac{\frac{1-5\sqrt{2}}{4-4\sqrt{2}}}{\sqrt{2}}=x=side\]

Answer 6

^4 that and "simplify" :)

Answer 7

or rather; *4 that and then ^4 it ... :/

Answer 8

ill get it eventually lol; *4 that and ^2 it

Answer 9

\[\dfrac{\frac{1-5\sqrt{2}}{4-4\sqrt{2}}}{\sqrt{2}}\]
\[\frac{1-5\sqrt{2}}{4\sqrt{2}-4(2)}\]
\[\frac{1-5\sqrt{2}}{4(\sqrt{2}-2)}*4\]
\[\frac{1-5\sqrt{2}}{\sqrt{2}-2}=p\]

Answer 10

so...

(1-5*square root 2)/(4-4*square root2) = (p sqrt2)/2

now we cancel 2...
(1-5*square root 2)/(2-2*square root2) = (p sqrt2)

divide both sides by sqrt 2

(1-5*square root 2)/(2sqrt 2-4) = p

square both sides...
p^2 = (1-5sqrt2)^2/(2sqrt2 - 4)^2

(1 -10sqrt2 + 100)/(8 -16sqrt2 + 16) = p^2

Answer 11

\[\left(\frac{1-5\sqrt{2}}{\sqrt{2}-2}\right)^2=p^2\]
\[\frac{1-10\sqrt{2}+250}{2-4\sqrt{2}+4}=p^2\]
maybe

Answer 12

lol...all three of us had different answers :)) this question is tricky

Answer 13

i think he missed a "2" to begin with;

"2"51-10sqrt(2) would make our answers match; not ours but mine and his :)

Answer 14

yours and mine differ by about 44 :)

http://www.wolframalpha.com/input/?i=%284*%281-5sqrt%282%29%29%2F%284sqrt%282%29-4%282%29%29%29%5E2+-+%281+-10sqrt2+%2B+100%29%2F%288+-16sqrt2+%2B+16%29

Answer 15

http://www.wolframalpha.com/input/?i=+1%2F8+%288%2B9+sqrt%282%29%29+-+%28%281-5sqrt%282%29%29%2F%284sqrt%282%29-4%282%29%29%29

wolfs simplification of :

s=1/8 (8+9sqrt(2))

seems to zero out with mine; just saying ;)