An architect is recreating the blueprint for a deck with an existing scale factor of 1 in. equals 2 ft​, that is shown. The architect is using a different scale so that the length of the same deck on the new blueprint measures 8 inches. Complete parts a and b. What is the scale factor of the new blue print? 1 inch = feet. Part 2: What is the width of the deck on the new​ blueprint?

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+

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