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# In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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09 Sep 2018, 06:52
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35% (medium)

Question Stats:

73% (02:11) correct 27% (02:09) wrong based on 79 sessions

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In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is a point on AD such that AO = 2 and the area of triangle BOC represents 75% of the area of triangle ABC. What is the area of ABC?

A. 7
B. 14
C. 21
D. 28
E. 56

Attachment:

image045.jpg [ 2.8 KiB | Viewed 808 times ]

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 951
WE: Supply Chain Management (Energy and Utilities)
Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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09 Sep 2018, 08:19
Bunuel wrote:

In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is a point on AD such that AO = 2 and the area of triangle BOC represents 75% of the area of triangle ABC. What is the area of ABC?

A. 7
B. 14
C. 21
D. 28
E. 56

Area of triangle ABC=1/2*BC*AD=1/2*7*(2+OD)=1/2*7*2+1/2*7*OD=7+Area of triangle BOC

Or, Area of triangle ABC=7+75% of the area of triangle ABC
Or, Area of triangle ABC=7+$$\frac{3}{4}$$*area of triangle ABC
Or, $$\frac{1}{4}$$ * Area of triangle ABC=7
Or, Area of triangle ABC=7*4=28

Ans. (D)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 28 Aug 2018
Posts: 3
GMAT 1: 520 Q30 V32
GMAT 2: 500 Q34 V24
Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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25 Nov 2018, 22:38
This my approach:
First I find the area of the 25% of the triangle and then work out the remaining 75%

(BC*AO)/2
7*2/2= 7

As 7 is the area of 25% of the triangle ABC. I worked out that the total area of the triangle is 28

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Joined: 24 Jan 2017
Posts: 13
Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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16 Dec 2018, 12:36
Bunuel wrote:

In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is a point on AD such that AO = 2 and the area of triangle BOC represents 75% of the area of triangle ABC. What is the area of ABC?

A. 7
B. 14
C. 21
D. 28
E. 56

Attachment:
image045.jpg

Area of BOC= 75% of Area of ABC

Since base is same in both triangles; 7, we need to find heights. Let us assume OD=H, and AD=AO+OD, also we know AO=2, so the height of ABC is H+2

Putting the values in equation above:

(1/2)(7)*H= 75% * (1/2)(7)*(H+2)
H=3/4*(H+2)
4H=3H+6
H=6.............

As we know height of ABC is H+2=6+2=8

So area of ABC= 1/2(7)(8)= 28

Manager
Joined: 18 Apr 2018
Posts: 97
In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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17 Dec 2018, 06:40
PKN wrote:
Bunuel wrote:

In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is a point on AD such that AO = 2 and the area of triangle BOC represents 75% of the area of triangle ABC. What is the area of ABC?

A. 7
B. 14
C. 21
D. 28
E. 56

Area of triangle ABC=1/2*BC*AD=1/2*7*(2+OD)=1/2*7*2+1/2*7*OD=7+Area of triangle BOC

Or, Area of triangle ABC=7+75% of the area of triangle ABC
Or, Area of triangle ABC=7+$$\frac{3}{4}$$*area of triangle ABC
Or, $$\frac{1}{4}$$ * Area of triangle ABC=7
Or, Area of triangle ABC=7*4=28

Ans. (D)

Hello PKN, please help me understand how you got the area of 25% of the triangle to be 7. I will be grateful, thanks.

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 951
WE: Supply Chain Management (Energy and Utilities)
Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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18 Dec 2018, 19:44
Kem12 wrote:
PKN wrote:
Bunuel wrote:

In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is a point on AD such that AO = 2 and the area of triangle BOC represents 75% of the area of triangle ABC. What is the area of ABC?

A. 7
B. 14
C. 21
D. 28
E. 56

Area of triangle ABC=1/2*BC*AD=1/2*7*(2+OD)=1/2*7*2+1/2*7*OD=7+Area of triangle BOC

Or, Area of triangle ABC=7+75% of the area of triangle ABC
Or, Area of triangle ABC=7+$$\frac{3}{4}$$*area of triangle ABC
Or, $$\frac{1}{4}$$ * Area of triangle ABC=7
Or, Area of triangle ABC=7*4=28

Ans. (D)

Hello PKN, please help me understand how you got the area of 25% of the triangle to be 7. I will be grateful, thanks.

Posted from my mobile device

Hi Kem12,

Please go through my explanation(highlighted in yellow color), suppose area of triangle ABC is x sq. units:

$$x=7+\frac{3}{4}*x$$
Or, $$(1-\frac{3}{4})*x=7$$
Or, $$\frac{1}{4}*x=7$$
Or, 25% of area of triangle ABC=7

Hope it helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is &nbs [#permalink] 18 Dec 2018, 19:44
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# In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is

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