Question

triangle ABC is similar to triangle DEF. if AB=10cm, DE=12cm, perimeter of triangle ABC=25cm, find the perimeter of triangle DEF​

Answer 1

Answer:

Step-by-step explanation:

ΔABC ~ ΔDEF

⇒ AB/DE = k

∴ 10/12 = 5/6

let P pe perimeter of ΔDEF

∴ 25/P = 5/6

⇒ P = 25 * 6 / 5

  = 30cm

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Answer 2

The perimeter of triangle DEF=30 cm

Step-by-step explanation:

Perimeter of triangle ABC=AB+BC+AC=25 cm

AB=10 cm

DE=12 cm

Triangle ABC is similar to triangle DEF

When two triangles ABC and DEF are similar then

$\frac{perimeter\;of\;triangle ABC}{perimeter\;of\;triangle DE F}=\frac{side\;of\;triangle ABC}{Side\;of\;triangle DE F}$

Substitute the values

$\frac{25}{Perimeter\;of\;triangle\;DE F}=\frac{AB}{DE}=\frac{10}{12}$

Perimeter of triangle DEF=$25\times \frac{12}{10}=30 cm$

Hence, the perimeter of triangle DEF=30 cm

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