perplexus.info :: Just Math : Polygon Perimeter

Polygon Perimeter (Posted on 2024-02-19)

The curve C has equation 2x² + 2xy + 5y² = 20.

The points on C for which both the x and y coordinates are integers are the vertices of a convex polygon P.

Find the exact perimeter of polygon P.

No Solution Yet Submitted by Danish Ahmed Khan

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finding the perimeter

| Comment 2 of 4 |

A graph shows an ellipse contained within -4<x<4 and -3<y<3, providing the search area.

fimplicit(@(x,y)2*x.^2+2*x.*y+5*y.^2-20);

grid

for x=-4:4

for y=-3:3

if 2*x^2+2*x*y+5*y^2==20

disp([x y])

end

>> polygonPerimeter

-2 2

0 -2

0 2

2 -2

(-2,2) to (0,2) and (0,-2) to (2,-2) provide two segments of length 2.

(-2,2) to (0,-2) and (0,2) to (2,-2) provide two segments of length sqrt(20).

The perimeter is 2*(2 + sqrt(20)) =~ 12.9442719099992.

Posted by Charlie on 2024-02-19 09:04:33

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