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ABC and AED are straight lines.



BE and CD are parallel.




AC = 12.3cm



AB = 8.2cm



BE = 3.8cm



a) Work out length CD.




AD = 9.15cm



b) Work out length ED.

Respuesta :

sqdancefan

Answer:

  • CD = 5.7 cm
  • ED = 3.05 cm

Step-by-step explanation:

a) ΔACD ~ ΔABE so the ratios of corresponding sides are the same. That is ...

  CD/BE = CA/BA

  CD/3.8 = 12.3/8.2

  CD = 3.8×12.3/8.2 = 5.7 . . . . cm

__

b) As above, the ratios of corresponding sides are the same.

  ED/AD = BC/AC

  ED/9.15 = (12.3-8.2)/12.3 . . . . BC = AC - AB

  ED = 9.15×4.1/12.3 = 3.05 . . . . cm

Ver imagen sqdancefan
akposevictor

Applying the knowledge of similar triangles to find the missing lengths:

a. the length of CD = 5.7 cm

b. the length of ED = 3.05 cm

The information for this problem has been put into a diagram for easy understanding (see attachment below).

Apply the knowledge of similar triangles to workout the lengths of CD and ED respectively.

Note:

  • Similar triangles will have the ratio of their corresponding sides equal to each other.
  • Triangle ABE and triangle ACD are similar triangles.

Since Triangles ABE and ACD are similar triangles, therefore:

  • AB/AC = AE/AD = BE/CD

a. Find the length of CD:

  • Use AB/AC = BE/CD

AB = 8.2 cm

AC = 12.3 cm

BE = 3.8 cm

CD = ?

  • Substitute:

[tex]\frac{8.2}{12.3} = \frac{3.8}{CD}[/tex]

  • Cross multiply

[tex]\frac{8.2}{12.3} = \frac{3.8}{CD}\\\\CD = \frac{3.8 \times 12.3}{8.2} = 5.7 $ cm[/tex]

b. Find the length of ED:

  • ED = AD - AE

AD = 9.15 cm

  • Let's find AE:

AB/AC = AE/AD

  • Substitute

[tex]\frac{8.2}{12.3} = \frac{AE}{9.15}[/tex]

  • Cross multiply

[tex]AE = \frac{8.2 \times 9.15}{12.3} = 6.1 $ cm[/tex]

ED = AD - AE

  • Substitute

ED = 9.15 - 6.1 = 3.05 cm

Therefore, applying the knowledge of similar triangles to find the missing lengths:

a. the length of CD = 5.7 cm

b. the length of ED = 3.05 cm

Learn more here:

https://brainly.com/question/16956655

Ver imagen akposevictor

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