Respuesta :

sqdancefan

Answer:

  • AB = 4 2/3
  • BC = 11 2/3
  • FC = 21
  • ED = 30

Step-by-step explanation:

In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.

Proportional segments

Segments of transversals crossed by parallel lines are proportional:

  AG : GF : FE = AB : BC : CD

  2 : 5 : 3 = AB : BC : 7

Multiplying the first ratios by 2 1/3 will give the second ratios:

  2 : 5 : 3 = 4 2/3 : 11 2/3 : 7

This lets us conclude ...

  AB = 4 2/3

  BC = 11 2/3

Similar triangles

Corresponding segments of similar triangles are proportional:

  AG : GB = FA : FC = AE : ED

  2 : 6 = (5+2) : FC = (5+2+3) : ED

We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...

  2 : 6 = 7 : 21 = 10 : 30

This lets us conclude ...

  FC = 21

  ED = 30

The lengths of the missing sides are calculated to be

  • AB = 5
  • BC = 12
  • FC = 21
  • ED = 30

How to find the lengths of the missing sides

The parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal

The given dimensions that is used to find the missing sides

Solving for AB

AB / CD = AG / FE

AB / 7 = 2 / 3

cross multiplying

3 * AB = 7 * 2

AB = 14/3 = 4.667

Using AB, GF is calculated

AB / BC = AG / GF

14/3 / BC = 2 / 5

cross multiplying

BC = (5 * 14/3) / 2

BC = 35/3 = 11.667

Solving for FC

GB / FC = AG / A'F

6 / FC = 2 / (2 + 5)

cross multiplying

2 * FC = 6 * 7

FC = 42/2 = 21

Solving for ED

GB / ED = AG / AE

6 / ED = 2 / (2 + 5 + 3)

cross multiplying

2 * ED = 6 * 10

ED = 60/2 = 30

Learn more about similar polygons at:

https://brainly.com/question/1493409

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