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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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estudierBest ResponseYou've already chosen the best response.3
dw:1350379170293:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Bad drawing, u probably should do your own.....:)
 one year ago

estudierBest ResponseYou've already chosen the best response.3
If u can see it opposite edges of the wood are aligned with corners of tile.
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
dw:1350379418357:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.3
@JamesWolf U should be practicing your Python!:)
 one year ago

estudierBest ResponseYou've already chosen the best response.3
That pic is not correct, the edges are aligned with the corners, not in the middle...
 one year ago

JamesWolfBest 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
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
opposite corners, yes i should be doing python! stupid python
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
i think dw:1350379781386:dw is the same as dw:1350379796776:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.3
dw:1350379795901:dw
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
asin, there is the same amount of mising area
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
dw:1350379782354:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.3
@sara12345 Yes, like that
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
dw:1350379878261:dw i think the two diagrams are equivilant
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
dw:1350379928886:dw
 one year ago

estudierBest ResponseYou've already chosen the best response.3
@JamesWolf I don't mind how u do it, your choice....
 one year ago

estudierBest ResponseYou've already chosen the best response.3
@sara12345 What r u going to do about the little corner bits?
 one year ago

JamesWolfBest 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?
 one year ago

estudierBest 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.
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
\[A = \frac{1}{2}(l  \frac{\sin\frac{\pi}{4}}{2})^2  l^2\]
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
that formula makes me think im wrong lol
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
whats your method estudier?
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Let's wait, let people have a go first.....
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
\[A = (\frac{1}{2}l  \frac{\sin\frac{\pi}{4}}{2})^2  l^2\]
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
alright so for a square with side length 5, i get  14. lol
 one year ago

estudierBest ResponseYou've already chosen the best response.3
I haven't done it with figures, let me check....
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
try with side length 5
 one year ago

estudierBest ResponseYou've already chosen the best response.3
I get a proportion of 1/4
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
of width of wood to area?
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Proportion of area covered by wood
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
i get 1/3.888 you got exactly 1/4?
 one year ago

estudierBest ResponseYou've already chosen the best response.3
dw:1350381191180:dw
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
\[2(\frac{1}{2} \times (l  \sqrt(2))^2)\] area not covered.
 one year ago

estudierBest ResponseYou've already chosen the best response.3
OK, unless someone comes with answer in a minute, I will post answer...
 one year ago

estudierBest ResponseYou've already chosen the best response.3
dw:1350381831150:dw
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
i think i see what your going to do!
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
hmm, not sure how your going to get XC
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
if thats what your going to do...
 one year ago

estudierBest ResponseYou've already chosen the best response.3
A longer way is to first see that APX and XBC are similar...
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
Im not very good at geometry so im not sure how that helps
 one year ago

estudierBest 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
 one year ago

estudierBest ResponseYou've already chosen the best response.3
It is also a //gram with base XC and height 1
 one year ago

estudierBest ResponseYou've already chosen the best response.3
So xa = sqrt((xa)^2 +a^2) Square and simplify gives you a quadratic...
 one year ago

estudierBest ResponseYou've already chosen the best response.3
a is side of square, you changed it to l
 one year ago

estudierBest 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
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Solving the quadratic and calculating the proportion gives 2/ (sqrt(2a^21) + 1)
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
we wil get x/a = 1/4 ?
 one year ago

estudierBest ResponseYou've already chosen the best response.3
That was for a = 5 only....
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
if i go ahead and solve the quadratic, ilg et x/ = 2/ (sqrt(2a^21) + 1) ?
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
x/a = 2/ (sqrt(2a^21) + 1)
 one year ago

estudierBest 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
 one year ago

JamesWolfBest 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)
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Both sides are the area of the parallelogram (the wood area) Base * "height"
 one year ago

JamesWolfBest ResponseYou've already chosen the best response.1
or just write on here :) dw:1350382973068:dw
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
dw:1350383010964:dw
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
for that gram, if we see bottom as base, then height = a
 one year ago

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

estudierBest ResponseYou've already chosen the best response.3
Good geometry practice:)
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
as of now im not getting how to simplify quadratic formula.. il work later
 one year ago

estudierBest ResponseYou've already chosen the best response.3
Hang on I will put the quadratic.....
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
i got : x^2(1a^2) + 2ax + 2a^2 = 0
 one year ago

sara12345Best ResponseYou've already chosen the best response.0
x^2(1a^2)  2ax + 2a^2 = 0
 one year ago

estudierBest 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...
 one year ago
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