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|dw:1350379170293:dw|

Bad drawing, u probably should do your own.....:-)

If u can see it opposite edges of the wood are aligned with corners of tile.

|dw:1350379418357:dw|

@JamesWolf U should be practicing your Python!:-)

That pic is not correct, the edges are aligned with the corners, not in the middle...

righttt sorry

opposite corners, yes i should be doing python! stupid python

:-)

i think |dw:1350379781386:dw|
is the same as |dw:1350379796776:dw|

|dw:1350379795901:dw|

asin, there is the same amount of mising area

|dw:1350379782354:dw|

like this ?

@sara12345 Yes, like that

|dw:1350379878261:dw|
i think the two diagrams are equivilant

|dw:1350379928886:dw|

@JamesWolf I don't mind how u do it, your choice....

@sara12345 What r u going to do about the little corner bits?

\[A = \frac{1}{2}(l - \frac{\sin\frac{\pi}{4}}{2})^2 - l^2\]

that formula makes me think im wrong lol

whats your method estudier?

Let's wait, let people have a go first.....

\[A = (\frac{1}{2}l - \frac{\sin\frac{\pi}{4}}{2})^2 - l^2\]

alright so for a square with side length 5, i get - 14. lol

I haven't done it with figures, let me check....

try with side length 5

I get a proportion of 1/4

of width of wood to area?

Proportion of area covered by wood

i get 1/3.888 you got exactly 1/4?

|dw:1350381191180:dw|

\[2(\frac{1}{2} \times (l - \sqrt(2))^2)\] area not covered.

OK, unless someone comes with answer in a minute, I will post answer...

:)

|dw:1350381831150:dw|

A minute plz

i think i see what your going to do!

estudier that is.

hmm, not sure how your going to get XC

if thats what your going to do...

A longer way is to first see that APX and XBC are similar...

Im not very good at geometry so im not sure how that helps

But a quicker way is to note that the wood area is a //gram with base x and height a

It is also a //gram with base XC and height 1

So xa = sqrt((x-a)^2 +a^2)
Square and simplify gives you a quadratic...

sorry, what is a?

a = A

a is side of square, you changed it to l

side of square

oh right sorry lol

carry on

You can get the same quadratic by similar triangles as I said before:
sqrt(x^2-1)/1 = (a-x)/a

Solving the quadratic and calculating the proportion gives 2/ (sqrt(2a^2-1) + 1)

we wil get
x/a = 1/4
?

That was for a = 5 only....

if i go ahead and solve the quadratic,
ilg et
x/ = 2/ (sqrt(2a^2-1) + 1)
?

x/a = 2/ (sqrt(2a^2-1) + 1)

No, you will get x = (an expression) but we want a proportion so multiply by a and divide by a^2

Both sides are the area of the parallelogram (the wood area)
Base * "height"

or just write on here :) |dw:1350382973068:dw|

|dw:1350383010964:dw|

for that ||gram, if we see bottom as base, then height = a

so sqrt((x-a)^2 +a^2) is working out the length from X to C

correct

then height =1

okay I see thanks

Good geometry practice:-)

as of now im not getting how to simplify quadratic formula.. il work later

yesss

back to python :)

Hang on I will put the quadratic.....

i got :
x^2(1-a^2) + 2ax + 2a^2 = 0

x^2(1-a^2) - 2ax + 2a^2 = 0