What is the perimeter of triangle ADC? (1) AD is a median in ΔABC.

Question

https://gmatclub.com/forum/download/file.php?id=61987 What is the perimeter of triangle ADC? (1) AD is a median in ΔABC. (2) The perimeter of ΔABC is 18. Project DS Butler Data Sufficiency (DS3) For DS butler Questions Click Here 1.png

rajatchopra1994 · Answer

To Find: the perimeter of triangle ADC

(1) AD is a median in ΔABC.
No data regarding sides.
Not Sufficient.

(2) The perimeter of ΔABC is 18.
No data regarding AD length.
Not Sufficient.

Combining 1 & 2,
Still not sufficient

IMO-E

sumitkrocks · Answer

Both statements combined we do not know AB and AC; Hence, Option  (E)  is correct

Note: If ABC were an an isosceles triangle with Sides AB and AC as equal, the two statements combined would have fetched answer (C)

errorlogger · Answer

1)AD= Median
CD = BD - Insufficient, as length of the sides are mentioned.
2)Perimeter of the triangle = 18 - Insufficient, as we need the perimeter for ADC
Combining 1 & 2:
CD = BD and triangle's peri = 18
We need AC = AB, to say ADC = 9, since it's not given
E IMO!

thelonghalloween · Answer

Not 100% sure of this, cause looks easy on face of it..

In the triangle ABC, lets say AB = a, BC = B and CA = c; DA = d; CD = e

So we are asked to find a + e + d

Statement 1: Doesn't really give any numerical information  Insufficient  
Statement 2: a + b + c = 18. Still D is unknown.  Insufficient

Both together: 
a + b + c = 18
e = b/2

4 variables and 2 equations --> Can't solve.  Insufficient  
 
Hence E

Aryan1991 · Answer

Could someone please help in understanding that in case the area of the triangle was given would then the area of the bisected triangle be half of the given triangle??

Fdambro294 · Answer

The median of any triangle will cut the triangle into two subdivided triangles with equal area.

This is because the median, by its definition, bisects the side it intersects. Therefore use that bisected side as the base for each of the 2 subdivided triangles.

Then, from one point to a line, there exists only one perpendicular height. So from that equal base to the vertex the median comes from ———-> the height drawn perpendicular will be the same for each of the subdivided triangles.

Since the bases are equal and the height is the same ——-> median creates two triangles of equal area.

Note: this does not mean the two triangles are congruent. Only in the case of an isosceles or equilateral triangle will the median create two congruent triangles.

Try drawing it out. Hopefully that helps somewhat?

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What is the perimeter of triangle ADC? (1) AD is a median in ΔABC.

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GMAT Data Sufficiency (DS) Questions

What is the perimeter of triangle ADC? (1) AD is a median in ΔABC.

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