Melody

I think that you have misinterpreted what she was trying to tell you. 

That is my only explanation.  Sorry. 

Hi Haley,

Area is the number of squares that fit inside a 2dimensional shape.

Here is a pink peice of paper.  Each one of those little squares is 1cm by 1cm  which means each one is $$1cm^2$$

Now you can count the squares - There are 36 of them so the Area must be $$36cm^2$$

Now how can we get this just with the length of the sides?

There are 12 squares in the top row. And there are 3 rows. So that must be 12+12+12 squares altogether.

or more simply   $$12\times 3 =36cm^2$$

So the area of a rectangle is length x breadth and the answer will be in units squared     $$u^2$$

Hi Jebus,

why don't you join up, it is very easy.  Then we wiill all know who you are every time. :)

Never mind Chris I gave you points anyway lol

I am quite enjoying the two of us answering questions with different approaches.

It opens up horizons. 

You can think of it like this

0,    1,   2,  ......................49

100,99,98,........................51

--------------------------------add

100+100+100..................100 ,    The only missing number is 50

So answer must be 100*50+50=5050

Hi Heureka,

Here are the rules listed at the top of the post

You do not have to use every number but you cannot use any number twice.

So you found all those wonderful solutions and you were making the question harder than it even needed to be.  

30mod2 = 0 because 30 divided by 2 = 15 with zero left over.

With modular arithmetic you only care about the remainder.  

Mmm interesting.

I have drawn this to scale.

Use Cosine Rule to find R

To get the 130degrees I used the fact that interior angles on parallel lines are Supplementary.

$$\\R^2=50^2+300^2-(2*50*300*cos130^0)\\
R^2=111783\\
R=334.34 \;km/hour$$

Now find the angle at the top of the triangle - Use Cosine Rule again.

I forgot to label it on the diagram but i have called it $$\alpha$$  in the working.

$$\\50^2=300^2+334.34^2-2*300*334.34*Cos(\alpha)\\\\
\alpha=acos\left(\frac{334.34^2+300^2-50^2}{2*300*334.34}\right)\\\\
\alph=6.578^0\\\\
therefore\\\\
\theta=30-6.578=23.42^0$$

$$So the plane is travelling S 23.4$^0$ W at 334km/hour$$

Note: I have not checked my working.    Any questions?  Just ask.

They are fabulous answers Heureka.

I think I got a different one again for the 821 magic number one. 

Anyway here are the solutions that I had.  They have been hiding all this time on an invisable post :)

These videos were  from an Australian show called "Letters and Numbers"

Lily Serna is awesome.     another solution to 821 is  also really 'out there'