Need a detailed solution for the below problem
What is the side of the square of the largest size that can be symmetrically inscribed in
an equilateral triangle of side 12?
OA [spoiler]12√3 / (2 + √3)[/spoiler]
Geometry
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- cans
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what do you mean by symmetrically inscribed?
Because if a square is inscribed i think it means that all the four corners lie on triangle. and there are only 3 sides.
Because if a square is inscribed i think it means that all the four corners lie on triangle. and there are only 3 sides.
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but that's not symmetrical.
(Y and Z have different view)
(Y and Z have different view)
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If you take this figure,
let side of square=x. then 12 = x + 2XA (XA=DZ)
also tan 60 = x/XA -> XA = x/root(3)
12 = x + 2x/(root(3))
x = [12*root(3)] / (2 + root(3))
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tdkk123 wrote:Need a detailed solution for the below problem
What is the side of the square of the largest size that can be symmetrically inscribed in
an equilateral triangle of side 12?
OA [spoiler]12√3 / (2 + √3)[/spoiler]
Since the sides of the square in the figure above must be equal:
x√3 = 12-2x
2x + x√3 = 12
(2+√3)x = 12
x = 12/(2+√3).
Thus, each side of the square = x√3 = 12√3/(2+√3).
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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