Polygons
The 8 eyelets for the lace of a sneaker all lie on a rectangle, four equally spaced on each of the longer sides. The rectangle has a width of 50 mm and a length of 80 mm. There is one eyelet at each vertex of the rectangle. The lace itself must pass between the vertex eyelets along a width side of the rectangle and then crisscross between successive eyelets until it reaches the two eyelets at the other width side of the rectrangle as shown. After passing through these final eyelets, each of the ends of the lace must extend at least 200 mm farther to allow a knot to be tied. Find the minimum length of the lace in millimeters.
The answer is 790.
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1 solution
Rectangle is divided into three smaller triangles with a width of 50 mm and a length of 80/3 mm. Since it is based on pythagorean theorem, the diagonal of this rectangle is sq.rt. of 50 raised to 2+ 80 squared over 3=170/3mm. it is hard to explain but it is a lace that is why , there are 6 of these diagonals, with a width, and at least 200 mm extension on each side. Therefore I conclude that the minimum of the lace in millimeters is 6x170/3 + 50 + 200 x 2 = 790