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Triangle ABC is similar to triangle DEF.
Which proportion can be used to find the length of DE in centimeters?
4. DE
* om min

Triangle ABC is similar to triangle DEF Which proportion can be used to find the length of DE in centimeters 4 DE om min class=

Respuesta :

Answer:

DE = 12 cm

Step-by-step explanation:

It is given that, [tex]\triangle ABC[/tex] is similar to  triangle DEF

For similar triangles, the corresponding sides are in same ratio. It means:

[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}[/tex]

We have,

AB = 4 cm

BC = 3 cm

EF = 9 cm

AC = 5 cm

DF = 15 cm

We need to find DE, use :

[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}\\\\\dfrac{4}{DE}=\dfrac{3}{9}\\\\\dfrac{4}{DE}=\dfrac{1}{3}\\\\DE=12\ cm[/tex]

So, the length of DE = 12 cm

The length of DE in centimetres is 12 .

The following proportion can be established as follow:

AB / DE = BC  / EF = AC / DF

Therefore,

let's find DE as follows;

AB  / DE = BC / EF

4 / DE = 3 / 9

cross multiply

9 × 4 = 3DE

divide both sides by 3

DE = 36 / 3

DE = 12 cm

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