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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: 50670
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
00:00

Difficulty:

25% (medium)

Question Stats:

88% (01:57) correct 12% (03:16) wrong based on 25 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

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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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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)
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Re: In the above triangle ABC, BC = 7, AD is perpendicular to BC and O is &nbs [#permalink] 09 Sep 2018, 08:19
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