I need help figuring this problem out.
A golden rectangle has a shorter side of 100 feet. How long is the longer side? Give your answer approximated to three decimal places.
2006-09-10 13:00:22 · 5 answers · asked by Ryan H 2 in Science & Mathematics ➔ Mathematics
Hi. A golden rectangle has sides which have the ratio (1+√5)/2. Remember this and you'll have learned something. Hint; Your short side is 100 feet, your long side is 100 times (1+√5)/2.
2006-09-10 13:04:53 · answer #1 · answered by Cirric 7 · 0⤊ 0⤋
A rectangle is a golden rectangle if its sides are in the ratio of phi to 1, where phi is the golden ratio, defined as the positive solution to x^2 - x - 1 = 0, or (-1+sqrt(5))/2 = 1.618033989...
So set up a proportion:
phi/1 = x/100,
where x is the other side of the rectangle. You use x/100, not 100/x, since you are given the shorter side, and 1 is smaller than phi. Solve the equation for x.
2006-09-10 20:05:18 · answer #2 · answered by alnitaka 4 · 0⤊ 0⤋
A golden rectangle is one where, if x is the short side, and y the long side, then x/y = (y-x)/x. Since you know that the short side is 100 feet, put 100 in the place of x and solve for y.
Good luck!
2006-09-10 20:09:28 · answer #3 · answered by KhiDhala 2 · 0⤊ 0⤋
In a golden rectangle the quotient longside/shortside must be the golden number phi = 1.61803398875... or (1+sqrt(5))/2
if the longside = 100 feet, then 100/shortside = 1.61803398875...
And shortside = 100/1.618033... = 61.803 feet
2006-09-10 20:09:34 · answer #4 · answered by vahucel 6 · 0⤊ 0⤋
draw a square 100ft by 100ft
the length of the longer side of the golden rectangle
is the diagonal of the square you have just drawn.
if you know your pythagorus you will be able to solve this.
2006-09-10 20:05:17 · answer #5 · answered by roos_rule06 2 · 0⤊ 0⤋