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 2 years 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?
 2 years 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?

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

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

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

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

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

JamesWolf
 2 years ago
Best ResponseYou've already chosen the best response.1so 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

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

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

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

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

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

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

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

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

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

JamesWolf
 2 years ago
Best ResponseYou've already chosen the best response.1how 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?

estudier
 2 years ago
Best ResponseYou've already chosen the best response.3I 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

estudier
 2 years ago
Best ResponseYou've already chosen the best response.3x = 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...
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