Question

Please help !!!
Violet runs on a triangular track in a local park. On Saturday, she runs one lap around track BAC. The length of each path on this track is shown in meters (m) in the diagram below. If track DEF is similar in shape to track BAC, how many meters, rounded to the nearest tenth, would Violet run in one lap on track BAC?

Answer 1

BAC and DEF are SIMILAR in shapes
that means they're the same shape, just at a different "ratio"

so, a 2x2 shape, will be SIMILAR to a 4x4 shape, with a ratio of 2
that is
2x2 is really = 2(2)x2(2)

Answer 2

look at the picture above, I simply flipped the big one to show you the SIMILAR sides

Answer 3

oh! thank you!!!

Answer 4

$$
\cfrac{18}{12}= \cfrac{b}{27}\\
\cfrac{18}{12}= \cfrac{a}{18}
$$

Answer 5

so, just solve for "a" and "b", and you'd get the sides of the longer track triangle

how long does Violet run on a lap?

18 + a + b

Answer 6

I think it's 48?

Answer 7

$$
\cfrac{18}{12}= \cfrac{b}{27} \implies b = \cfrac{18\times 27}{12} \implies 40.5\\
\cfrac{18}{12}= \cfrac{a}{18} \implies a = \cfrac{18 \times 18}{12} \implies 27
$$

Answer 8

thanks, i know what i did wrong