A little algebra ii - Can u solve it

[limbei]

let me see...
The square is cut diagonally with the length of the diameter of the circle, 2.
By Pythagoras thm, base sq+ height sq = Diagonal sq
x sq + x sq = 2sq
2x sq = 4
x sq = 2
x = sq root 2
= 1.14

[RyusRevenge]

Ok if it was a square embedded onto the circle than its easy,

2cos45 = height
2sin45 = width

cant be bothered to look it up in the calculator, u can do that yourself .

btw if youcant work out how i come to this conclusion its simple, if a square is embedded onto the circle (i.e the corners of the square are touching the line of the circle) the diagnol across the square is the same as the diameter of the circle, therefore u are able to split the square into 2 equal triangles, the radius of the circle is 1, therefore the diameter is 2.

diameter 2 = hypotenuse

a square has 90 degrees at each vertex, since we split it into 2 equal triangles, it has become an acute angle of 45 degrees.

So now we have 2 vital peices of info, the hypotenuse which is 2 and the acute angle of the triangle which is 45 degrees, simple pythagoras can be used to work out the other two sides - width and height.



Edited By RyusRevenge on 1099727907

[TarkanX]

Like a few have explained, since the radius of the circle is one, the diameter of the circle is two, and if the diameter of the circle is two, then the hypotenuse of the sliced square (cut diagnolly) is two. So it would be:

a^2 + b^2 = c^2

= a^2 + b^2 = 2^2

a = b, so...

(2a^2 = 4) / (2)

= a^2 = 2

Square root both and you get:

a = square root of 2, let's see if this is correct.

v - represents square root of.

v2^2 + v2^2 = 2^2

2 + 2 = 4.

We are right, so the length and width would be v2, which is approximately 1.4142.



Edited By TarkanX on 1099766839

[KenDaShoto]

yea thats what i put on the test but im not sure if thats right
and units dont matter and thats all the info we got so stop askin for more



Edited By KenDaShoto on 1099770511

[blossom]

runs far away*

[Saijin_Ryu]

[quoteost_uid0="TarkanX"]Like a few have explained, since the radius of the circle is one, the diameter of the circle is two, and if the diameter of the circle is two, then the hypotenuse of the sliced square (cut diagnolly) is two. So it would be:

a^2 + b^2 = c^2

= a^2 + b^2 = 2^2

a = b, so...

(2a^2 = 4) / (2)

= a^2 = 2

Square root both and you get:

a = square root of 2, let's see if this is correct.

v - represents square root of.

v2^2 + v2^2 = 2^2

2 + 2 = 4.

We are right, so the length and width would be v2, which is approximately 1.4142.[/quote]
The bits in italic is what i understood up too.

[KenDaShoto]

well i expected to post the answer today but my teacher didnt come to school today so maybe tomorrow

[QUIET_KILLER]

[quoteost_uid0="TarkanX"]Like a few have explained, since the radius of the circle is one, the diameter of the circle is two, and if the diameter of the circle is two, then the hypotenuse of the sliced square (cut diagnolly) is two. So it would be:

a^2 + b^2 = c^2

= a^2 + b^2 = 2^2

a = b, so...

(2a^2 = 4) / (2)

= a^2 = 2

Square root both and you get:

a = square root of 2, let's see if this is correct.

v - represents square root of.

v2^2 + v2^2 = 2^2

2 + 2 = 4.

We are right, so the length and width would be v2, which is approximately 1.4142.[/quote]
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Edited By QUIET_KILLER on 1099950199

[KenDaShoto]

good thing quiet killer cause before i saw that u were just kidding u made me want to close the topic before i gave the answer

[KenDaShoto]

still hasnt given back the test and wont til friday so.... yeah