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problem 94 · 5 lines

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<p>It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the <dfn>almost equilateral triangle</dfn> $5$-$5$-$6$ has an area of $12$ square units.</p>
<p>We shall define an <dfn>almost equilateral triangle</dfn> to be a triangle for which two sides are equal and the third differs by no more than one unit.</p>
<p>Find the sum of the perimeters of all <dfn>almost equilateral triangles</dfn> with integral side lengths and area and whose perimeters do not exceed one billion ($1\,000\,000\,000$).</p>
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