Mathematics, 07.07.2020 16:01 Carrchris021

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.

a) Work out the length of DE.
b) Work out the l

Answers: 3

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Answer from: Jasten

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

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Answer from: andersonkee2657

Step-by-step explanation:

The trick here is to notice that :

$\frac{AB}{DC}$ = $\frac{BC}{DE}$ = $\frac{AC}{CE}$

Now let's replace by the values we khow :

$\frac{AB}{18}$ = $\frac{8}{24}$ = $\frac{5}{DE}$ 8/24 is 1/3 to make it simple Now AB= 18*(1/3)=6 AND DE= 5*(3/1)=15

So AB=6 cm and DE=15 cm

Answer from: Quest

huh? im pretty sure it is in 199

step-by-step explanation:

Answer from: Quest

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf =

pf = 6,25 u

ver más en -

step-by-step explanation:

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

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