Question

similar triangles

Answer 1

@phi

Answer 2

can you try to match up red sides with blue sides?
any idea which side matches up with k ?

Answer 3

or I should say, k matches up with which blue side ?

Answer 4

wait:/ I thought I was doing it in steps like 13/6

Answer 5

yes, we can do that if you like.
Pick a side in the red triangle (I always try to pick out something like "longest" or shortest" if I can)

Answer 6

There are 3 sides in the red triangle. Pick out the longest side.

Answer 7

13/26

Answer 8

yes, that is longest red / longest blue

now I would see if I can match up the k in the red with the correct side in the blue
The k side looks like it's the shortest leg, so I would match it with the shortest leg in the blue

Answer 9

k/6

Answer 10

now set them equal
and solve for k

Answer 11

k/6=13/26?

Answer 12

yes, exactly.
now multiply both sides by 6 to find k

Answer 13

3

Answer 14

yes

Answer 15

are you willing to do one more with me?