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estudier
Group Title
Piece of wood width 1 sits over a square tile through opposite corners (see pic)
What proportion of the area of the tile is covered by the wood?
 2 years ago
 2 years ago
estudier Group Title
Piece of wood width 1 sits over a square tile through opposite corners (see pic) What proportion of the area of the tile is covered by the wood?
 2 years ago
 2 years ago

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estudier Group TitleBest ResponseYou've already chosen the best response.3
dw:1350379170293:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Bad drawing, u probably should do your own.....:)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
If u can see it opposite edges of the wood are aligned with corners of tile.
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
dw:1350379418357:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
@JamesWolf U should be practicing your Python!:)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
That pic is not correct, the edges are aligned with the corners, not in the middle...
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
so a is the angle between the middle of the wood and the side of the square which is 90/2 = 45. the bottom of that triangle has length 1/2. we need to find b. then you can do "length of square"  b = side of triangledw:1350379684247:dw
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
righttt sorry
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
opposite corners, yes i should be doing python! stupid python
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
i think dw:1350379781386:dw is the same as dw:1350379796776:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
dw:1350379795901:dw
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
asin, there is the same amount of mising area
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
dw:1350379782354:dw
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
like this ?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
@sara12345 Yes, like that
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
dw:1350379878261:dw i think the two diagrams are equivilant
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
dw:1350379928886:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
@JamesWolf I don't mind how u do it, your choice....
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
@sara12345 What r u going to do about the little corner bits?
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
how about i do it my way, and sara can do it her way, and we will both solve for area. and see if they really are equivilant?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
I will tell u there is there is also a quick way to do it but I will give medal for correct answer by any method.
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
\[A = \frac{1}{2}(l  \frac{\sin\frac{\pi}{4}}{2})^2  l^2\]
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
that formula makes me think im wrong lol
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
whats your method estudier?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Let's wait, let people have a go first.....
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
\[A = (\frac{1}{2}l  \frac{\sin\frac{\pi}{4}}{2})^2  l^2\]
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
alright so for a square with side length 5, i get  14. lol
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
I haven't done it with figures, let me check....
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
try with side length 5
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
I get a proportion of 1/4
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
of width of wood to area?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Proportion of area covered by wood
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
i get 1/3.888 you got exactly 1/4?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
dw:1350381191180:dw
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
\[2(\frac{1}{2} \times (l  \sqrt(2))^2)\] area not covered.
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
OK, unless someone comes with answer in a minute, I will post answer...
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
dw:1350381831150:dw
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.0
A minute plz
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
i think i see what your going to do!
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
estudier that is.
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
hmm, not sure how your going to get XC
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
if thats what your going to do...
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
A longer way is to first see that APX and XBC are similar...
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
Im not very good at geometry so im not sure how that helps
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
But a quicker way is to note that the wood area is a //gram with base x and height a
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
It is also a //gram with base XC and height 1
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
So xa = sqrt((xa)^2 +a^2) Square and simplify gives you a quadratic...
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
sorry, what is a?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
a is side of square, you changed it to l
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
side of square
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
oh right sorry lol
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
You can get the same quadratic by similar triangles as I said before: sqrt(x^21)/1 = (ax)/a
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Solving the quadratic and calculating the proportion gives 2/ (sqrt(2a^21) + 1)
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
we wil get x/a = 1/4 ?
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
That was for a = 5 only....
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
if i go ahead and solve the quadratic, ilg et x/ = 2/ (sqrt(2a^21) + 1) ?
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
x/a = 2/ (sqrt(2a^21) + 1)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
No, you will get x = (an expression) but we want a proportion so multiply by a and divide by a^2
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
sorry as i said im rubbish, can you explain what side each term is refering too in this So xa = sqrt((xa)^2 +a^2)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Both sides are the area of the parallelogram (the wood area) Base * "height"
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
or just write on here :) dw:1350382973068:dw
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
dw:1350383010964:dw
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
for that gram, if we see bottom as base, then height = a
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
so sqrt((xa)^2 +a^2) is working out the length from X to C
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
then height =1
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
okay I see thanks
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Good geometry practice:)
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
as of now im not getting how to simplify quadratic formula.. il work later
 2 years ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.1
back to python :)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
Hang on I will put the quadratic.....
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
i got : x^2(1a^2) + 2ax + 2a^2 = 0
 2 years ago

sara12345 Group TitleBest ResponseYou've already chosen the best response.0
x^2(1a^2)  2ax + 2a^2 = 0
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.3
x = a(1 + sqrt(2a^21) ) / ( a^21) (dropping the  soln) Multiply by a, divide by a^2 > (sqrt(2a^21) 1) / (a^21) > equivalent what I gave before...
 2 years ago
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