From the given information in the diagram
a) The length of DE is 15cm and
b) The length of AB is 6cm
From the question,
Triangles ABC and CDE are mathematically similar.
a) To determine the length of DE
Since ΔABC is similar to ΔCDE
By similar triangles theorem, we can write that
[tex]\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}[/tex]
From the diagram
/BC/ = 5cm
/CA/ = 8cm
/EC/ = 24 cm
/DE/ = ?
Putting these values into
[tex]\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}[/tex]
We get
[tex]\frac{5}{/DE/}=\frac{8}{24}[/tex]
∴ [tex]8 \times /DE/ = 5 \times 24[/tex]
Now, divide both sides by 8
[tex]\frac{8 \times /DE/}{8}= \frac{5 \times 24}{8}[/tex]
[tex]/DE/ = \frac{120}{8}[/tex]
/DE/ = 15cm
b) To work out the length of AB
Also, by similar triangles theorem, we can write that
[tex]\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}[/tex]
From the diagram
/AB/ = ?
/CD/ = 18cm
/CA/ = 8cm
/EC/ = 24 cm
Putting these values into
[tex]\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}[/tex]
We get
[tex]\frac{/AB/}{18}=\frac{8}{24}[/tex]
Now, multiply both sides by 18, that is
[tex]18 \times \frac{/AB/}{18}=\frac{8}{24} \times 18[/tex]
[tex]/AB/ = \frac{144}{24}[/tex]
/AB/ = 6cm
Hence,
a) The length of DE is 15cm and
b) The length of AB is 6cm
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