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ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. cm (2) AC = 6.15 cm. (b) Work out the length of AB.​

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akposevictor

By applying the knowledge of similar triangles, the lengths of AE and AB are:

a. [tex]\mathbf{AE = 3.9 $ cm}\\\\[/tex]

b. [tex]\mathbf{AB = 2.05 $ cm} \\\\[/tex]

See the image in the attachment for the referred diagram.

  • The two triangles, triangle AEC and triangle BDC are similar triangles.
  • Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.

This implies that:

  • AC/BC = EC/DC = AE/DB

Given:

[tex]EC = 8.1 $ cm\\\\DC = 5.4 $ cm\\\\DB = 2.6 cm\\\\AC = 6.15 $ cm[/tex]

a. Find the length of AE:

EC/DC = AE/DB

  • Plug in the values

[tex]\frac{8.1}{5.4} = \frac{AE}{2.6}[/tex]

  • Cross multiply

[tex]5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06[/tex]

  • Divide both sides by 5.4

[tex]AE = \frac{21.06}{5.4} = 3.9 $ cm[/tex]

b. Find the length of AB:

[tex]AB = AC - BC[/tex]

AC = 6.15 cm

To find BC, use AC/BC = EC/DC.

  • Plug in the values

[tex]\frac{6.15}{BC} = \frac{8.1}{5.4}[/tex]

  • Cross multiply

[tex]BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1[/tex]

  • Thus:

[tex]AB = AC - BC[/tex]

  • Substitute

[tex]AB = 6.15 - 4.1\\\\AB = 2.05 $ cm[/tex]

Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:

a. [tex]\mathbf{AE = 3.9 $ cm}\\\\[/tex]

b. [tex]\mathbf{AB = 2.05 $ cm} \\\\[/tex]

Learn more here:

https://brainly.com/question/14327552

View image akposevictor
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