Mathematics, 26.06.2019 15:10 dantelin123

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.

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Answer from: ravenl1001

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:

$\frac{8.2}{12.3} = \frac{3.8}{CD}$

Cross multiply

$\frac{8.2}{12.3} = \frac{3.8}{CD}\\\\CD = \frac{3.8 \times 12.3}{8.2} = 5.7 $ cm$

b. Find the length of ED:

ED = AD - AE

AD = 9.15 cm

Let's find AE:

AB/AC = AE/AD

Substitute

$\frac{8.2}{12.3} = \frac{AE}{9.15}$

Cross multiply

$AE = \frac{8.2 \times 9.15}{12.3} = 6.1 $ cm$

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

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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 ou

Answer from: juliaduenkelsbu

CD = 5.7 cmED = 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

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