Question

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.​

Answer 1

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

a. $\mathbf{AE = 3.9 cm}$

b. $\mathbf{AB = 2.05 cm}$

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:

$EC = 8.1 cm\\\\DC = 5.4 cm\\\\DB = 2.6 cm\\\\AC = 6.15 cm$

a. Find the length of AE:

EC/DC = AE/DB

• Plug in the values

$\frac{8.1}{5.4} = \frac{AE}{2.6}$

• Cross multiply

$5.4 \times AE = 8.1 \times 2.6\\\\5.4 \times AE = 21.06$

• Divide both sides by 5.4

$AE = \frac{21.06}{5.4} = 3.9 cm$

b. Find the length of AB:

$AB = AC - BC$

AC = 6.15 cm

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

• Plug in the values

$\frac{6.15}{BC} = \frac{8.1}{5.4}$

• Cross multiply

$BC \times 8.1 = 6.15 \times 5.4\\\\BC = \frac{6.15 \times 5.4}{8.1} \\\\BC = 4.1$

• Thus:

$AB = AC - BC$

• Substitute

$AB = 6.15 - 4.1\\\\AB = 2.05 cm$

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

a. $\mathbf{AE = 3.9 cm}$

b. $\mathbf{AB = 2.05 cm}$

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