Question

similar triangles?

Answer 1

@phi

Answer 2

what is the shortest side in the red triangle, and what is the shortest in the blue triangle ?

Answer 3

3, 9.

Answer 4

yes, but the order matters, and I am doing red:blue so 9:3
or 9/3

next, we need to match up the k side in the red triangle with the correct side in the blue triangle

Answer 5

it's a bit hard to say whether the k goes with the 4.5 or the 4 side
so let's try Plan B

we first simplify 9/3 to 3
next we test the 12 side in the red triangle with 4.5 and with 4
12/4.5 or 12/4
we know we have the correct match if it simplifies to 3 (just like 9/3 simplified to 3)

12/4 = 3

that means 12 matches up with the 4

and that also means k matches up with 4.5

Answer 6

now we can do the problem
\[ \frac{k}{4.5}= \frac{9}{3} \]
multiply both sides by 4.5 to find k

Answer 7

13.5

Answer 8

yes