Question

A golden rectangle has side lengths in the ratio of about 1 : 1.618. If the long side of a golden rectangle is 35 cm, what is its area? Round your answer to the nearest tenth.

Answer 1

In a golden rectangle, the side lengths are in the ratio \[\text{short:long} \approx 1:1.618\]or written as fractions

\[\frac{\text{short}}{\text{long}} = \frac{1}{1.618}\]You know what the long side is, so plug it into the equation, cross-multiply and solve for the short side.

Answer 2

21.632= shortside?

Answer 3

The exact value is \[1:\frac{1+\sqrt{5}}{2}\]which has an unending decimal representation. One of the many nifty things about it is that if you take the reciprocal of \(\phi = 1.618...\) you get the same string of digits after the decimal point!

\[1.6180339887498948482045868343656381177203091798057628621354486227\]\[0.6180339887498948482045868343656381177203091798057628621354486227\]

You are close: correct manipulation, but haven't followed the directions on rounding your answer...

Answer 4

There's a fun book on the Golden Ratio: http://www.amazon.com/The-Golden-Ratio-Worlds-Astonishing/dp/1469286092

Answer 5

A. 2450 cmlook at the picture
B. 757.1 cmlook at the picture
C. 612.5 cmlook at the picture
D. 1982.1 cmlook at the picture

Answer 6

ignore the look at the picture part
but the answers are to the second power

Answer 7

okay, so you have the long side = 35 and the short side = 21.6 and you need the area.

area of a rectangle is given by \[A = l*w\]

Answer 8

i got 756

Answer 9

35*21.632 = 757.12

Don't round until you reach the final answer to prevent loss of accuracy such as you experienced.

Answer 10

oh ok thank you very much!

Answer 11

You're welcome!