Two boards are placed end to end to make a walkway. One board is 5 feet 11 inches long, and the other board is 4 feet 6 inches long. How long is the walkway? Write your answer in feet and inches. Use a number less than 12 for inches.

Answer is in the file below

https://cutt.ly/kzjInUL

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