Mr. john doe was figuring out his federal income tax. his income was $26,800, but he was able to subtract $5,500 in deductions. he paid 15% of the remaining income tax. how much did he pay?

Okay so the income tax minus the deductions will come to:

26,800 - 5,500 = 21,300

So remaining tax is 21,300.

To show that he paid 15% of it, we do:

15/100 (21300) = 3,195

So he already paid $3,195 of his income tax.

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