anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1350379170293:dw|
anonymous
  • anonymous
Bad drawing, u probably should do your own.....:-)
anonymous
  • anonymous
If u can see it opposite edges of the wood are aligned with corners of tile.

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More answers

anonymous
  • anonymous
|dw:1350379418357:dw|
anonymous
  • anonymous
@JamesWolf U should be practicing your Python!:-)
anonymous
  • anonymous
That pic is not correct, the edges are aligned with the corners, not in the middle...
anonymous
  • anonymous
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 triangle|dw:1350379684247:dw|
anonymous
  • anonymous
righttt sorry
anonymous
  • anonymous
opposite corners, yes i should be doing python! stupid python
anonymous
  • anonymous
:-)
anonymous
  • anonymous
i think |dw:1350379781386:dw| is the same as |dw:1350379796776:dw|
anonymous
  • anonymous
|dw:1350379795901:dw|
anonymous
  • anonymous
asin, there is the same amount of mising area
anonymous
  • anonymous
|dw:1350379782354:dw|
anonymous
  • anonymous
like this ?
anonymous
  • anonymous
@sara12345 Yes, like that
anonymous
  • anonymous
|dw:1350379878261:dw| i think the two diagrams are equivilant
anonymous
  • anonymous
|dw:1350379928886:dw|
anonymous
  • anonymous
@JamesWolf I don't mind how u do it, your choice....
anonymous
  • anonymous
@sara12345 What r u going to do about the little corner bits?
anonymous
  • anonymous
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?
anonymous
  • anonymous
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.
anonymous
  • anonymous
\[A = \frac{1}{2}(l - \frac{\sin\frac{\pi}{4}}{2})^2 - l^2\]
anonymous
  • anonymous
that formula makes me think im wrong lol
anonymous
  • anonymous
whats your method estudier?
anonymous
  • anonymous
Let's wait, let people have a go first.....
anonymous
  • anonymous
\[A = (\frac{1}{2}l - \frac{\sin\frac{\pi}{4}}{2})^2 - l^2\]
anonymous
  • anonymous
alright so for a square with side length 5, i get - 14. lol
anonymous
  • anonymous
I haven't done it with figures, let me check....
anonymous
  • anonymous
try with side length 5
anonymous
  • anonymous
I get a proportion of 1/4
anonymous
  • anonymous
of width of wood to area?
anonymous
  • anonymous
Proportion of area covered by wood
anonymous
  • anonymous
i get 1/3.888 you got exactly 1/4?
anonymous
  • anonymous
|dw:1350381191180:dw|
anonymous
  • anonymous
\[2(\frac{1}{2} \times (l - \sqrt(2))^2)\] area not covered.
anonymous
  • anonymous
OK, unless someone comes with answer in a minute, I will post answer...
anonymous
  • anonymous
:)
anonymous
  • anonymous
|dw:1350381831150:dw|
anonymous
  • anonymous
A minute plz
anonymous
  • anonymous
K
anonymous
  • anonymous
i think i see what your going to do!
anonymous
  • anonymous
estudier that is.
anonymous
  • anonymous
hmm, not sure how your going to get XC
anonymous
  • anonymous
if thats what your going to do...
anonymous
  • anonymous
A longer way is to first see that APX and XBC are similar...
anonymous
  • anonymous
Im not very good at geometry so im not sure how that helps
anonymous
  • anonymous
But a quicker way is to note that the wood area is a //gram with base x and height a
anonymous
  • anonymous
It is also a //gram with base XC and height 1
anonymous
  • anonymous
So xa = sqrt((x-a)^2 +a^2) Square and simplify gives you a quadratic...
anonymous
  • anonymous
sorry, what is a?
anonymous
  • anonymous
a = A
anonymous
  • anonymous
a is side of square, you changed it to l
anonymous
  • anonymous
side of square
anonymous
  • anonymous
oh right sorry lol
anonymous
  • anonymous
carry on
anonymous
  • anonymous
You can get the same quadratic by similar triangles as I said before: sqrt(x^2-1)/1 = (a-x)/a
anonymous
  • anonymous
Solving the quadratic and calculating the proportion gives 2/ (sqrt(2a^2-1) + 1)
anonymous
  • anonymous
we wil get x/a = 1/4 ?
anonymous
  • anonymous
That was for a = 5 only....
anonymous
  • anonymous
if i go ahead and solve the quadratic, ilg et x/ = 2/ (sqrt(2a^2-1) + 1) ?
anonymous
  • anonymous
x/a = 2/ (sqrt(2a^2-1) + 1)
anonymous
  • anonymous
No, you will get x = (an expression) but we want a proportion so multiply by a and divide by a^2
anonymous
  • anonymous
sorry as i said im rubbish, can you explain what side each term is refering too in this So xa = sqrt((x-a)^2 +a^2)
anonymous
  • anonymous
Both sides are the area of the parallelogram (the wood area) Base * "height"
anonymous
  • anonymous
or just write on here :) |dw:1350382973068:dw|
anonymous
  • anonymous
|dw:1350383010964:dw|
anonymous
  • anonymous
for that ||gram, if we see bottom as base, then height = a
anonymous
  • anonymous
so sqrt((x-a)^2 +a^2) is working out the length from X to C
anonymous
  • anonymous
correct
anonymous
  • anonymous
then height =1
anonymous
  • anonymous
okay I see thanks
anonymous
  • anonymous
Good geometry practice:-)
anonymous
  • anonymous
as of now im not getting how to simplify quadratic formula.. il work later
anonymous
  • anonymous
yesss
anonymous
  • anonymous
back to python :)
anonymous
  • anonymous
Hang on I will put the quadratic.....
anonymous
  • anonymous
i got : x^2(1-a^2) + 2ax + 2a^2 = 0
anonymous
  • anonymous
x^2(1-a^2) - 2ax + 2a^2 = 0
anonymous
  • anonymous
x = a(-1 + sqrt(2a^2-1) ) / ( a^2-1) (dropping the - soln) Multiply by a, divide by a^2 -> (sqrt(2a^2-1) -1) / (a^2-1) -> equivalent what I gave before...

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