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In triangles △ABC and △DEF,

m∠A=m∠E, m∠C=m∠F,

AC=6, EF=2, and AB=3.3,

side DF is shorter than side BC by 3.2.

Find the unknown sides of these triangles.

Respuesta :

sqdancefan

Answer:

  • BC = 4.8
  • ED = 1.1
  • DF = 1.6

Step-by-step explanation:

Since angles A and E correspond, as well as angles C and F, we can say ...

  ΔABC ~ ΔEDF

Then the ratio of side lengths of ΔABC to those of ΔEDF is ...

  AC/EF = 6/2 = 3

That means ...

  ED/AB = 1/3

  ED = AB·(1/3) = 3.3·(1/3) = 1.1

For the remaining sides, we have the relation

  3·DF = BC

  3·(BC -3.2) = BC

  2BC - 9.6 = 0 . . . eliminate parentheses, subtract length BC

  BC -4.8 = 0 . . . . . divide by 2

  BC = 4.8 . . . . . . . . add 4.8

  DF = BC·(1/3) = 1.6

The unknown side lengths are BC = 4.8, DE = 1.1, DF = 1.6.

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