Find 4 consecutive even integers such that the sum of the third and fourth exceeds 1/3 of the first by the sum of the first and third

The three consecutive odd integers are 3,5,7

How:

Let x, (x+2),(x+4) represent the three consecutive odd integers

Question states***  

2[x + (x+4)] = (x+2) + 15

solving for s

 4x + 8 = x + 17

   3x = 9

    x = 3   The three consecutive odd integers are 3,5,7

geometry: triangles

solvers

lessons

answers archive

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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