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Product of the lengths of AD and BC

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by shashank.ism » Sun Feb 21, 2010 2:05 pm
Nijeesh wrote:Image

In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
(2) The length of BC is 8.
area = 1/2 x AD x BC
St.1) product of length of AC and BE = 60 --> Area = 1/2 x AC xBE = 1/2x 60 = 30
so ad x BC = 2 area = 2x 30 = 60
suff.
St2.) length of BC is 8 but length of AD is not known so insuff.

Ans A
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by harsh.champ » Sun Feb 21, 2010 2:14 pm
Nijeesh wrote:Image

In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
(2) The length of BC is 8.
Statement 1:-AC x BE =60
=>Area of Triangle = 1/2 x AC x BE =30
Also, 1/2 x AD x BC =Area of the triangle.
Hence sufficient.

Statement 2:- length of BC=8cm
From pythagorus theorem we can find the length of the altitude.
Sufficient.

Hence D is the answer.
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by shashank.ism » Sun Feb 21, 2010 2:29 pm
harsh.champ wrote: Statement 1:-AC x BE =60
=>Area of Triangle = 1/2 x AC x BE =30
Also, 1/2 x AD x BC =Area of the triangle.
Hence sufficient.

Statement 2:- length of BC=8cm
From pythagorus theorem we can find the length of the altitude.
Sufficient.

Hence D is the answer.
length of BC = 8 is given ..

but it is no where written that d is mid point BC .s o how will calculate AD by knowing the value of BC only ..is it because it is orthocentre...???
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by ajith » Sun Feb 21, 2010 7:34 pm
Nijeesh wrote:Image

In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
(2) The length of BC is 8.
1) AC*BE = 2*Area of the triangle = AD*BC ; Sufficient
2) BC =8; Insufficient

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by girish3131 » Mon Mar 08, 2010 6:00 am
but guys...

y u consider it's a equi lateral triangle.... ?

ta
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by papgust » Mon Mar 08, 2010 5:25 pm
I guess no one is considering this triangle an equilateral here. They are just calculating the area.
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by salmaan » Mon Mar 08, 2010 7:42 pm
Hey:

Just posting for the sake of a different viewpoint.

At first I thought Statement 2 might be sufficient with the help of Statement 1. So I looked at Statement 1...

AC*BE = bh
now...rotate the triangle so CB is the base
It's the same triangle, so
AD*BC = bh. That is what we are looking for.

Thus AC*BE = AD*BC = 60!
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by bpgen » Mon Mar 08, 2010 9:36 pm
Appreciate everyone!

This is a guessing game Man!, nothing else...And I would go for answer D with assumption..

WITHOUT assumption, answer would be E, nothing is sufficient.

In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
[who told AC and BE are perpendicular similarly AD and BC as well? Nothing mentioned in question.
So let's assume and then ARG-1 would be sufficient. ]

(2) The length of BC is 8.
[Assume triangle is equilateral and AD is perpendicular to BC, who told? Nobody..just assuming..ok man! go ahead! :-)
Then knowing AB(=BC), BD(=1/2BC), we could find AD, huhh... ]
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by salmaan » Tue Mar 09, 2010 3:19 pm
they must be perpendicular because the question states that they are right angles.

i agree with shashank.ism and ajith.
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by Shawshank » Wed Mar 10, 2010 2:37 am
It is mentioned in the diagram that both the angles are perpendicular..

IMO -- A

No where is it mentioned that D is the midpoint.
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by blaster » Thu Mar 11, 2010 2:58 am
so,what is the correct OA?
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by salmaan » Sun Mar 14, 2010 6:03 pm
Why does it matter what the midpoint is? BH/2 = area. That's all you need to know.
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by fluke » Sun Jan 30, 2011 5:32 am
OA: A

Q: What is AD*BC


I.
(1/2)*AC*BE=(1/2)*BC*AD [Area of triangle will be the same]
AC*BE=BC*AD
AC*BE=60
Therefore, BC*AD=60. Found the answer to the question. Sufficient.

II. BC=8. Don't know whether BC=AC or DE=BE. This triangle can be formed in many ways each having different BE, AD, AC and BC. Not sufficient.
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by GMATGuruNY » Sun Jan 30, 2011 1:56 pm
Nijeesh wrote:Image

In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
(2) The length of BC is 8.
No math is needed here.

Any side of a triangle can be considered the base, and each base has a corresponding height.
To draw the height that corresponds to a given base, start at the vertex opposite the base and draw a line that forms a right angle with the base.

In the triangle above:
BE is the height that corresponds to base AC.
AD is the height that corresponds to base BC.

We know that A = 1/2*b*h. No matter which base and corresponding height are used, the area must remain the same. Thus, AC*BE = BC*AD.

Statement 1: AC*BE = 60
Thus, BC*AD = 60.
Sufficient.

Statement 2: BC = 8
No way to determine AD.
Insufficient.

The correct answer is A.
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