The town of Hillsville has a triangular walking trail, as shown on the left. Perry wants to construct a similar trail in his town, but he has only enough space for a base of 280

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

to find the perimeter, you add up all the lengths of the sides. in this case you would have to add up 18+22+40+80 which equals 160.