Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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.​

Sagot :

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
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.