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Bunuel
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Bunuel
can you explain this ques ?


The midpoints of 3 sides of the triangle ABC are respectively D, E, F. What is the perimeter of triangle ABC?

Given that D, E, and F are the midpoints of sides AB, AC, and BC, respectively, we know that DE, DF, and EF are midsegments of triangle ABC. By the midsegment theorem, which states that the midsegment is always half the length of the third side, we have 2DE = BC, 2DF = AC, and 2EF = AB. The perimeter of ABC = BC + AC + AB = 2DE + 2DF + 2EF = 2(DE + DF + EF) = 2*(perimeter of triangle DEF). Therefore, to find the perimeter of ABC, we need to find the perimeter of DEF.

(1) The perimeter of the triangle DEF is 10.

Sufficient.

(2) The length of the side AC is 4.

This is clearly insufficient.

Answer: A.
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