A cleaning solution is made from vinegar, lemon juice, and water. The table below shows the part of the total solution that is in each element. Solution Components Solution A Solution B Solution C Vinegar 0. 1 0. 2 0. 4 Lemon Juice 0. 15 0. 2 0. 1 Water 0. 75 0. 6 0. 5 Mr. Allen needs 100 mL of a solution that is 30% vinegar, 15% lemon juice, and 55% water. How much of solution A will Mr. Allen need to make his cleaning solution?.

560

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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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)