Question

COULD SOMEONE PLEASE HELP ME?? WILL MEDAL!

Answer 1

http://assets.openstudy.com/updates/attachments/58514b6ae4b00a05d347867b-rz172-1481722737726-15400355_1291748410884936_2235951972265306778_n.png

Answer 2

@3mar

Answer 3

O.K. Now that I have had my coffee, and pondered the chart, I've discovered that they want the longest side for the length, and the shortest side for the width, regardless how its orientation on the page will change on the page as the aditional square is added. Do you agree?

Answer 4

Looking at stage 5 we see the length will be 8 and the width 5, stage 6 we see the length is now
(8 + 5) or 13 and the width is now 8 or 3 + 5. But we can also see or note the fact that the length has progressed like this 1, 2, 3, 5, 8, 13 does this progression look familiar
Also the the width progressed in a similar manner 1, 1, 2, 3, 5, the same kind of progression the next number will be the sum of the previous two numbers. This makes it easy now.

Answer 5

Using this discovery......the "Fibonacci" series....
Stage 6, length is 13, width is 8
Stage 7, length is 21, width is 13
Stage 8, length is 34, width is 21
Stage 9, length is 55, width is 34

Answer 6

I did not provide the length/width ratio as you can do this with you calculator after completing the length and width in the chart.

Answer 7

They are showing you that the "golden ratio" is also similar to the value obtained by dividing the two Fibonacci adjacent terms, with more accuracy as the series gets bigger and bigger.

Answer 8

Do you not see that progression??