In a triangle ABC, sinA : sinB : sinC = 1 : 2 : 3. If b = 4 cm, then the perimeter of the triangle is -

6 cm

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24 cm

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12 cm

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8 cm

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Solution

The correct option is B 12 cm
According to sin rule: $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$
$⟹ a$ $= 4 \times \frac{sin A}{sin B}, c = 4 \times \frac{sin C}{sin B} = 4 \times \frac{1}{2} = 2 c m c = 4 \times \frac{3}{2} = 6 c m$
$p e r i m e t e r = a + b + c = 2 + 4 + 6 = 12 c m$

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In $△$ ABC, AB = 3 cm, BC = 2 cm and CA = 2.5 cm. $△$ DEF is similar to $△$ ABC. If EF = 4 cm, then the perimeter of $△$ DEF is -

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{(a + b)}^{2} = c^{2} + a b

Given $△$ DEF $\sim$ $△$ ABC. If AB = 4 cm, BC = 2 cm, CA = 3 cm and EF = 4 cm, then the perimeter of $△$ DEF is ____ cm.

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