computergeek123 3 years ago The local community park is designing a pool using the Golden Ratio. If the pool is 110 feet wide, about how long should it be?

1. drpeppergal

What is the golden ratio?

2. pfenn1

The golden ratio is also called the divine proportion. It equals 1.618 (approx).

3. pfenn1

Assuming the length is larger than the width 1.618=x/110

4. drpeppergal

does it have any thing to do with fibonacci numbers?

5. bmp

^Yeah, that's how I would solve it too. :-)

6. estudier

a/b = 1/2(1+sqrt(5))

7. computergeek123

110 is not correct. :P

8. pfenn1

@drpeppergal , according to wikipedia, the ratio of sequential elements of the Fibonacci sequence approaches the golden ratio asymptotically.

9. bmp

It's 177.98 @computergeek123 :-)

10. bmp

1.618*110 = x

11. bmp

Typo: it should be \[\LARGE \Phi^n = Fib(n) \Phi + Fib(n-1) \]

12. estudier

Which side is which?

13. estudier

68 (approx) 110/68 = 1.618

14. computergeek123

so i woulld put 180?

15. estudier

OK, assuming one is less than other, I see now...

16. bmp

180 is too much rounding, I guess. 178 is better, but we are already rounding phi to 1.618 only :-)

17. estudier

I still say there are 2 answers, why should you divide length by width?

18. bmp

Sure, I agree @estudier. It's a pretty badly formulated question. @computergeek123 should pick between one of two. :-)

19. computergeek123

well theres 100, 120, 150 and 180 so i think 180 is best? @bmp

20. bmp

Yup, then it's

21. estudier

OK, assumed in the choices......grrr.

22. computergeek123

is this next one correct? Which number comes next in this sequence? 2, 5, 11, 23, 47 … Answer 68 82 95✔ 101

23. estudier

Double +1

24. bmp

Yeah, @estudier is correct. :-)

25. estudier

The tick was a clue:-)

26. computergeek123

Meg grows broccoli in a square plot in her garden. She created a drawing of her broccoli plot on a coordinate grid. The locations of three corners of the plot are represented by coordinates (3, 0), (1, 6), and (7, 8). Which of these coordinates represent the fourth corner? (8, 2) (8, 3) (9, 2)✔✔ (9, 3)

27. computergeek123

Bibi is using a software program that allows her to change the shape of a two-dimensional figure by making changes to the sides. She starts with a quadrilateral with opposite sides parallel. She stretches the shorter edges of the quadrilateral to make all four sides congruent. Which statement best describes the figure that she created? Answer She changed a kite to a square. She changed a rectangle to a square. She changed a trapezoid to a rhombus.✔ She changed a parallelogram to a rhombus.

28. bmp

The last one, it's just the definition of a trapezoid and a rhombus, so, it's correct :-)

29. computergeek123

So i have the correct answers??