In an equilateral △ABC of side 6 cm, D, E and F are the midpoints of sides BC, CA and AB respectively. The perimeter of △DEF is .

15 cm

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18 cm

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9 cm

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12 cm

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Solution

The correct option is C 9 cm
Given that,
The side of the equilateral triangle = 6 cm,
AB = BC = AC = 6 cm.
In △ABC,
F and E are the mid-points of AB and AC.
By mid point theorem,
$∴ E F = \frac{1}{2} B C = \frac{1}{2} \times 6 = 3 c m$
Similarly ED = DF = 3 cm
$∴$ Perimeter of △DEF = 3 $\times$ 3 = 9 cm

Hence, the perimeter of the △DEF is 9 cm.

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