Geometry. find the indicated side of the triangle. include a clear answer and description if possible.

That is a right isosceles triangle, also known as a 45 45 90 triangle.

In such a triangle, the sides "a" and "b" are equal and they equal the hypotenuse multiplied by 1 / sq rt(2) or 0.7071067812

Sides "a" and "b" equal 7.071067812

Source 1728.com/trig2.htm

the answer will be

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584