Question

$\triangle ABC \sim \triangle DEF$, ar($\triangle ABC$) = $9 cm^{2}$, ar($DEF$) = $16 cm^{2}$. If BC = 2.1 cm, then the measure of EF is
(a) 2.8 cm
(b) 4.2 cm
(c) 2.5 cm
(d) 4.1 cm

Answer 1

Answer:

The measure of EF is 2.8 cm.

Among the given options option (a) is 2.8 cm is the correct answer.

Step-by-step explanation:

Given:

ΔABC ~ ΔDEF.

Area of ΔABC = 9 cm².

Area of ΔDEF = 16 cm²

BC  = 2.1 cm

ar(ΔABC)/ar( ΔDEF) = (BC/EF)²

[The ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.]

9/16 = 2.1²/EF²

9/16 = (2.1/EF)²

(2.1/EF) = √9/16

(2.1/EF) = ¾  

3 EF = 4 × 2.1

EF = (4 × 2.1)/3

EF = 4 × 0.7

EF = 2.8 cm

Hence, the measure of EF is 2.8 cm.

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Answer 2

Answer:

EF = 2.8 cm

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