Mathematics: Triangles ABC and CDE are mathematically similar. a) Work out the length of DE. b) Work out the length of AB.

Triangles ABC and CDE are mathematically similar.

Ответ:

gerardogonzale2294

29.01.2022

Mathematics

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

$\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}$

From the diagram

/BC/ = 5cm

/CA/ = 8cm

/EC/ = 24 cm

/DE/ = ?

Putting these values into

$\frac{/BC/}{/DE/}=\frac{/CA/}{/EC/}$

We get

$\frac{5}{/DE/}=\frac{8}{24}$

∴ $8 \times /DE/ = 5 \times 24$

Now, divide both sides by 8

$\frac{8 \times /DE/}{8}= \frac{5 \times 24}{8}$

$/DE/ = \frac{120}{8}$

/DE/ = 15cm

b) To work out the length of AB

Also, by similar triangles theorem, we can write that

$\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}$

From the diagram

/AB/ = ?

/CD/ = 18cm

/CA/ = 8cm

/EC/ = 24 cm

Putting these values into

$\frac{/AB/}{/CD/}=\frac{/CA/}{/EC/}$

We get

$\frac{/AB/}{18}=\frac{8}{24}$

Now, multiply both sides by 18, that is

$18 \times \frac{/AB/}{18}=\frac{8}{24} \times 18$

$/AB/ = \frac{144}{24}$

/AB/ = 6cm

Hence,

a) The length of DE is 15cm and

b) The length of AB is 6cm

Learn more here: link

0,0(0 оценок)

Triangles ABC and CDE are mathematically similar. a) Work out the length of DE.
b) Work out the length of AB.

Ответ:

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question