Question 1134195: TriangleABC~DEF
If AB=3, DE=5, BC=9 find the length of EF.
Found 2 solutions by greenestamps, Theo:
Answer by greenestamps(13200)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! if the triangles are similar, then the corresponding sides are proportional.
this means that the corresponding sides from one triangle to the other have the same ratio.
this means that AB / DE = BC / EF = AC / DF
AB / DE = 3 / 5
BC / EF = 9 / x
x is chosen as the value for the length of EF that you want to solve for.
since the ratios have to be the same, you have 3 / 5 = 9 / x
cross multiply to get 3 * x = 5 * 9
simplify to get 3 * x = 45
solve for x to get x = 45 / 3 = 15
your solution is that the length of EF is equal to 15.
you have AB / DE = BC / EF which results in 3 / 5 = 9 / 15.
cross multiply to get 3 * 15 = 5 * 9 which results in 45 = 45, confirming the ratios are the same.
note that the naming conventions for congruent or similar triangle require that the letters designating the triangle are present in the order of the corresponding sides and angle.
this means that, if triangle ABC is similar to triangle DEF, then:
the corresponding sides are AB to DE, BC to EF, AC to DF and the corresponding angles are A to D, B to E, C to F.
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