Answer:
CD = 8 cm
Step-by-step explanation:
Given
See attachment
[tex]AE=6 cm,\ ED=4 cm,\ AB=4.5 cm,\ BE=4.8 cm.[/tex]
Required
Find CD
To calculate CD, we first calculate BC using the following equivalent ratio
[tex]AB : BC = AE:ED[/tex]
Substitute values for AB, AE and ED
[tex]4.5 : BC = 6 : 4[/tex]
Express as fraction
[tex]\frac{4.5 }{ BC} = \frac{6 }{ 4}[/tex]
Cross Multiply
[tex]BC * 6 = 4.5 * 4[/tex]
[tex]BC * 6 = 18[/tex]
Divide through by 6
[tex]BC = 3[/tex]
To calculate CD,
We make use of the following equivalent ratio
[tex]AB : BE = AC : CD[/tex]
Where
[tex]AC = AB + BC[/tex]
[tex]AC = 4.5 + 3[/tex]
[tex]AC = 7.5[/tex]
So, we have:
[tex]AB : BE = AC : CD[/tex]
[tex]4.5 : 4.8 = 7.5 : CD[/tex]
Express as fraction
[tex]\frac{4.5 }{ 4.8 }= \frac{7.5 }{ CD}[/tex]
Cross Multiply
[tex]4.5 * CD = 7.5 * 4.8[/tex]
Divide through by 4.5
[tex]CD = \frac{7.5 * 4.8}{4.5}[/tex]
[tex]CD = \frac{36}{4.5}[/tex]
[tex]CD = 8[/tex]
