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8,10,14,9,10

Step-by-step explanation:

these are the real answers

Explanation:

This is something you find out through trial and error. Sometimes you get lucky to spot the answer quickly, and other times it takes a while.

A useful trick in problem solving is to break things up into smaller parts, and see if there's a pattern going on.

Break up 28 into 2 and 8

Note that 5-3 = 2 and 5+3 = 8

So the conjecture is "the first part is the difference of the values; the second part is the sum of the values"

Let's test it

9-1 = 8 and 9+1 = 10. We combine those results getting 810. So that works

8-6 = 2 and 8+6 = 14. Those results lead to 214. That works as well.

5-4 = 1 and 5+4 = 9. This leads to 19. So far so good.

Assuming the pattern holds up, we have

7-3 = 4 and 7+3 = 10. So the value 410 would replace the question mark.

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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