Squeeze It In

Geometry Level pending

In a square of side length 30, can we fit an equilateral triangle of side length 32?

Yes No

Calvin Lin by Calvin Lin

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2 solutions

J Chaturvedi
Apr 9, 2016

No. The height of ∆ is 16√3. At that distance on the diagonal of the square, from a corner, the width available for triangle to fit in is 2(30√2-16√3) which is less than width of 32 required for the triangle.

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Md Islam
Apr 9, 2016

Let x be the highest possible side of ET to be fit into the square with side 30. Then (x^2-30^2)^(1/2)+x/2^(1/2)=30. So, x is less than or equal to 31.058285

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