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:
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
[tex]\frac{8.1}{5.4} = \frac{AE}{2.6}[/tex]
[tex]5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06[/tex]
[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.
[tex]\frac{6.15}{BC} = \frac{8.1}{5.4}[/tex]
[tex]BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1[/tex]
[tex]AB = AC - BC[/tex]
[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]
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