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Isosceles Triangle Within a Unit Cube (Posted on 2025-03-30)

Determine the largest area of an isosceles triangle that is enclosed within a unit cube.

What is the answer if the triangle is equilateral?

No Solution Yet Submitted by K Sengupta

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possible soln.s

| Comment 1 of 2

Isosceles: For the base, use the diagonal of the cube's base. Put the

apex on an opposed corner. The height is the distance between

(1/2, 1/2, 0) and (0, 0, 1) = sqrt(3/2), Area = (1/2) sqrt(2) sqrt(3/2)

Area = sqrt(3)/2

Equilateral: Use 3 non-planer vertices of the cube. Each side is sqrt(2).

Again, Area = sqrt(3)/2

Posted by Steven Lord on 2025-03-30 13:14:03

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