Answer:
- Timmy has successfully shown Suzie's conjecture is incorrect
- Suzie's conjecture is correct if the smallest square in the sum is 1
Step-by-step explanation:
The sum of odd numbers 1 .. n is ((n+1)/2)², a perfect square. Suzie is right about that. What Timmy has shown is that she is incorrect that the conjecture applies to <em>any</em> sum of consecutive odd numbers.
Timmy's sum of 5+7+9 is incorrect; it is 3·7 = 21. But, Timmy has the right idea. The sum of an arbitrary set of consecutive odd numbers will be the difference of two squares, but not necessarily a perfect square.
Area of kite is equal to 1/2 the product of the lengths of the diagonals
so
A=1/2(AD)(BF)
BF=BG+GF=8+8=18
AD=AG+GD=7+13.5=20.5
A=1/2(20.5)(18)=(8)(20.5)=164
now minus the area of the square
area of square=side^2=(CE)^2=9^2=81
kite-square=164-81=83 square meters
If both of the statistics in the question are accurate, then the land area of Florida is about 170,000 square kilometers. In order to come up with that number, I divided 1,700,000 by ten.
