We can't tell which rectangle is given as a golden rectangle. Plus, you
didn't tell us what " a ", and what, if anything, you are letting be 1.
Probably English is not your first language. That is OK!! It is my ONLY
language. J
I will assume that rectangle ACDF is given as a golden rectangle, and I will
assume that the length of a side of square ABEF is " a ". the shorter side of
rectangle BCDE is given as " 1 ".
By definition of 'golden rectangle':
Rectangle BCDE is similar to rectangle ACDF.
a. Show that
(a/1) = 1/(a - 1)
CROSS-MULTIPLY
<-- use this in part (b)
Divide both sides by (a-1)
b. Find the exact value of a(which will give you the golden ratio) by completing the square.
1. Get half of coefficient of a: (-1)/2 = -1/2
2. Square (-1/2), get +1/4
3. Add to both sides
Factor left side into the square of a binomial:
Take square roots of both sides, using ± on right.
Since ' a ' is not negative, we discard the - sign:
That is the exact value of ' a ', the golden ratio.
Edwin