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rxs0005
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vyassaptarashi
According to me theres some mistake in the question .... because according to the question CM and AN are medians ...then medians must intersect at the centroid which divides medians in 2:1 proportion and not equal ... hence k can not be the midpoint of the MC....

Please check the question ones again .... and if i am wrong then please explain....

It's not mentioned that AN is a median.

CM is definitely a median.
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some how it looks as if area is 3* area of triangle AKC = 3
option C.

still trying to figure it out though.
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fluke
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rxs0005
In Triangle ABC M is the mid point of segment AB

N is a point on segment BC

If CM and AN intersect at K which is the midpoint of MC

and AKC has area 1 what is the area of ABC

1

1/2

3

3.5

2

Area of ABC should be 4 as per the given conditions. Could you please recheck your question and options?
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Fluke

4 is there in the Answer choice i missed it can you please let us know how you came to that answer choice
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hurray finally got it.
I think it should be 4.

1. Concepts - Median divides a triangle into two triangles of equal areas.

For similar triangles 1 and 2 .... (Side of 1 / Side of 2 ) ^2 = Area of 1 / Area of 2.

2. Construction -- Draw a line from K to the midpoint of AC. Let the point of intersection be called as E.

Means KE || AM.

3. Similar Triangle Approach ---- Area of triangle AKC = 1 ,means Area of triangle AEK = Area of triangle CEK = 0.5 each

Tirangles CEK and CAM are Similar means
(CK/ CM) ^2 = Area of triangle CEK/ Area of triangle CEM

CK/CM = 1/2 means Area of CEK = 4* Area of triangle CEM

= 2

4.. Hence Area of triangle CAM = 2 Means Area of triangle ABC = 2 * Area of triangle CAM = 4

Thus B.
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Fluke

4 is there in the Answer choice i missed it can you please let us know how you came to that answer choice

Please find the image attached:
Attachment:
medians_and_area.PNG
medians_and_area.PNG [ 7.87 KiB | Viewed 1787 times ]

A median divides a triangle in two halves.

AKM=ACK=1 [Note: AK is the median as K is the midpoint of MC. Thus; AK divides AMC in two halves, viz. AKC and AKM]
Thus, AMC=AKM+ACK=1+1=2

AMC=BMC=2 [Note: CM is the median as M is the midpoint of AB. Thus; CM divides ABC in two halves, viz. AMC and BMC]
ABC = AMC+BMC = 2+2=4.

Ans: "B"
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Excellent fluke. +1 for you :)



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