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

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

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New post 09 Sep 2018, 07:52
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Question Stats:

73% (02:32) correct 27% (03:11) wrong based on 86 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
image045.jpg [ 2.8 KiB | Viewed 955 times ]

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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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New post 09 Sep 2018, 09:19
Bunuel wrote:
Image
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)
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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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New post 25 Nov 2018, 23:38
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

Answer is D

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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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New post 16 Dec 2018, 13:36
Bunuel wrote:
Image
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

D is answer
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In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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New post 17 Dec 2018, 07:40
PKN wrote:
Bunuel wrote:
Image
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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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is  [#permalink]

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New post 18 Dec 2018, 20:44
Kem12 wrote:
PKN wrote:
Bunuel wrote:
Image
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
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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is   [#permalink] 18 Dec 2018, 20:44
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In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is

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