Question

BE is parallel to CD.

Answer 1

Answer:

CD = 8 cm

Step-by-step explanation:

Given

See attachment

$AE=6 cm,\ ED=4 cm,\ AB=4.5 cm,\ BE=4.8 cm.$

Required

Find CD

To calculate CD, we first calculate BC using the following equivalent ratio

$AB : BC = AE:ED$

Substitute values for AB, AE and ED

$4.5 : BC = 6 : 4$

Express as fraction

$\frac{4.5 }{ BC} = \frac{6 }{ 4}$

Cross Multiply

$BC * 6 = 4.5 * 4$

$BC * 6 = 18$

Divide through by 6

$BC = 3$

To calculate CD,

We make use of the following equivalent ratio

$AB : BE = AC : CD$

Where

$AC = AB + BC$

$AC = 4.5 + 3$

$AC = 7.5$

So, we have:

$AB : BE = AC : CD$

$4.5 : 4.8 = 7.5 : CD$

Express as fraction

$\frac{4.5 }{ 4.8 }= \frac{7.5 }{ CD}$

Cross Multiply

$4.5 * CD = 7.5 * 4.8$

Divide through by 4.5

$CD = \frac{7.5 * 4.8}{4.5}$

$CD = \frac{36}{4.5}$

$CD = 8$