Question

triangle ABC ~ triangle DEF and the perimeter of triangle ABC and triangle DEF are 30 cm and 18 cm respectively. If BC = 9 cm the length of EF is
(A) 6.3 cm
(B) 5.4 cm
(C) 7.2 cm
(D) 4.5 cm
​

Answer 1

ABC Similar to DEF

so

BC / EF = Perimeter of ABC / Perimeter of DEF

Let EF = X

9/x = 30/18

9/X = 5/3

27 = 5x

X = 5.4 cm.

hope it may help you

Answer 2

(B) 5.4 cm

The length of EF =  5.4 cm.

Explanation:

Given :

ΔABC ~ Δ DEF and the perimeter of triangle ABC and triangle DEF are 30 cm and 18 cm respectively.

Here , segment BC corresponds to EF.

The length of BC = 9 cm

We know that the ratio of the corresponding sides of similar triangleis equal to the ratio of their perimeters.

⇒  $\dfrac{\text{Perimeter of triangle DE F} }{\text{Perimeter of triangle ABC}}=\dfrac{EF}{BC}$

$\Rightarrow\ \dfrac{18}{30}=\dfrac{EF}{9}\\\\\Rightarrow\ EF=\dfrac{18}{30}\times9=5.4$

Hence, the length of EF =  5.4 cm.

# Learn more :

If triangle ABC ~ triangle DEF, BC=6 cm. EF=8 cm, find the ratio of triangle ABC to triangle DEF

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