(adsbygoogle = window.adsbygoogle || []).push({}); Why is this answer incorrect? [Geometry]

---edited

I see where I went wrong, but with my current level of mathematical knowledge, I am at a dead end:

I do not know how do draw this question in ASCII, so I will describe it. There is an equilateral triangle with a square inscribed within it. The square has sides of 6 (cm), it asks how long each side of the triangle is. (NOTE: the top of the square fits perfectly to form another triangle, and the two sides of the square form 2 right triangles)

Now, in the top triangle, since it is as well equilateral, and the base (the top of the square) is 6, so the other sides must be 6.

-let y represent the hypotenuse of the two right triangles formed by the square and the larger triangle.

-let n represent the base of the two right triangles (the side other than that formed by the 6 cm side of the square)

-let x represent the side lengths of the larger equilateral triangle which the square is in.

(it would help to draw this while following along)

AXIOMS:

- [tex] x = 6 + y[/tex]

- [tex] n = ( x - 6 ) / 2 [/tex]

therefore [tex] n = [ ( y + 6 ) - 6 ] / 2

= y / 2 [/tex]

Now, with this all settled....

[tex]y^2 = 6^2 + n^2 [/tex]

[tex]y^2 = 36 + (y/2)^2 [/tex]

[tex]y^2 = 36 + (y^2 /4) [/tex]

[tex]y = \sqrt{36+(y^2/4)}[/tex]

[tex]y = \sqrt{ \frac {36} {1} + \frac {y^2} {4} }[/tex]

[tex]y = \sqrt{ \frac {144 + y^2} {4} }[/tex]

[tex]y = \frac { \sqrt{144+y^2} } {2} [/tex]

Is it possible to derive a value of [tex]y[/tex] from this?

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# Homework Help: Why is is this answer incorrect? [Geometry]

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