Hello, Moo!
3) Simple geometry
The Swedish flag has a yellow cross of constant width in a blue background.
The yellow area represents one-third of the flag's area.
If the flag is 1m long and 66cm wide, what is the width of the yellow stripes ?
The stripes comprising the cross can be "moved" to the edges of the flag.
Let $\displaystyle x$ = width of the stripe (cm). Code:
100
* - - - - - - - - *
| | x
| * - - - - - - *
66 | | |
| | | 66-x
| | |
* - * - - - - - - *
x 100-x
The blue region's area is: .$\displaystyle \frac{2}{3} \times (66\cdot100) \:=\;4400$ cm²
It is also: .$\displaystyle (100-x)(66-x)$ cm²
Hence, we have: .$\displaystyle (100-x)(66-x) \:=\:4400 \quad\Rightarrow\quad x^2 - 166x + 2200 \:=\:0$
The Quadratic Formula gives us: .$\displaystyle x \;=\;83 \pm3\sqrt{521}$
The smaller root is the answer: .$\displaystyle x \;=\;83 - 3\sqrt{521} \;\approx\;14.52$ cm.