Similar triangles may or may not be congruent
The length of CD is 49 units.
From the given triangles, we have the following equivalent ratios
[tex]\mathbf{AD:DE = AC:CB}[/tex]
Where:
[tex]\mathbf{AC = AD + CD}[/tex]
So, we have:
[tex]\mathbf{AD:DE = AD + DC:CB}[/tex]
Substitute known values
[tex]\mathbf{27:23 = 27 + DC:65}[/tex]
Express as fraction
[tex]\mathbf{\frac{27}{23} = \frac{27 + DC}{65}}[/tex]
Multiply both sides by 65
[tex]\mathbf{\frac{27}{23} \times 65= 27 + DC}[/tex]
Subtract 27 from both sides
[tex]\mathbf{\frac{27}{23} \times 65- 27 = DC}[/tex]
[tex]\mathbf{\frac{27\times 65}{23} - 27 = DC}[/tex]
[tex]\mathbf{\frac{1755}{23} - 27 = DC}[/tex]
[tex]\mathbf{76 - 27 = DC}[/tex]
[tex]\mathbf{49 = DC}[/tex]
Rewrite as:
[tex]\mathbf{CD = 49}[/tex]
Hence, the length of CD is 49 units.
Read more about similar shapes at:
https://brainly.com/question/14926756
