Given that triangle abc ~ triangle def, solve for x ... AB = 35 AC=49 BC=42 on the bigger triangle now on the smaller triangle DE = 5 what is EF for x the choices are 6, 7, 12, and 10

I'm similar. triangles all the corresponding angles are equal and the sides are all proportionate to some ratio and that ratio will be the same for all sides. since the order the triangle is written is ABC and DEF, AB would be proportionate to DE and BC is proportionate to EF. let's solve for what the ratio is.

we can say the ratio is x. all corresponding sides when compared would have to be equal to this ratio for the triangles to be similar so we can say

x = AB/DE

And

x = BC/EF

we know that x = x by logical reasoning. therefore

AB/DE = BC/EF

SO:

35/5 = 49/EF

7 = 49/EF

7 * EF = 49

EF = 7