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The midpoints of 3 sides of the triangle ABC are respectively D, E, F.

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Bunuel
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The midpoints of 3 sides of the triangle ABC are respectively D, E, F. [#permalink] New post   31 Jan 2023, 07:01
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The midpoints of 3 sides of the triangle ABC are respectively D, E, F. What is the perimeter of triangle ABC?

(1) The perimeter of the triangle DEF is 10
(2) The length of the side AC is 4


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Re: The midpoints of 3 sides of the triangle ABC are respectively D, E, F. [#permalink] New post   23 Feb 2023, 10:18
The midpoints of 3 sides of the triangle ABC are respectively D, E, F. What is the perimeter of triangle ABC?
From basic proportionality theorem(BPT) and converse of BPT, we know that DE// BC; DF//AC and EF//AB
Also, BC = 2DE; AC =2DF; AB = 2EF.
We need to find AB + BC + CA = 2 (DE+DF+EF)
(1) The perimeter of the triangle DEF is 10
Sufficient.
(2) The length of the side AC is 4
From this we can't find the values of the other two sides. Not Sufficient.
Answer A
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Re: The midpoints of 3 sides of the triangle ABC are respectively D, E, F. [#permalink] New post   08 Mar 2023, 11:28
Bunuel
can you explain this ques ?
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Re: The midpoints of 3 sides of the triangle ABC are respectively D, E, F. [#permalink] New post   08 Mar 2023, 12:30
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hasanijtaba wrote:
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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Re: The midpoints of 3 sides of the triangle ABC are respectively D, E, F. [#permalink]
08 Mar 2023, 12:30
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Bunuel
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