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.

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:

Since Triangles ABE and ACD are similar triangles, therefore:

a. Find the length of CD:

AB = 8.2 cm

AC = 12.3 cm

BE = 3.8 cm

CD = ?

b. Find the length of ED:

AD = 9.15 cm

AB/AC = AE/AD

ED = AD - AE

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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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

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: