The total length of three boards is 7/8 of a yard. The lengths of two of the boards are 1/4 of a yard and 3/16 of a yard. What is the length of the third board? *

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step-by-step explanation

2r= 2300

r =1150

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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