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# ABC is an equilateral triangle with point D on line BC such that AD =

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DS Forum Moderator
Joined: 22 Aug 2013
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Location: India
ABC is an equilateral triangle with point D on line BC such that AD =  [#permalink]

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17 Jul 2018, 23:22
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60% (00:48) correct 40% (01:06) wrong based on 10 sessions

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ABC is an equilateral triangle with point D on line BC such that AD = 4 units. What is the area of triangle ABC in square units?

(1) AD is perpendicular to BC.

(2) D is mid point of BC.
Math Expert
Joined: 02 Aug 2009
Posts: 6535
Re: ABC is an equilateral triangle with point D on line BC such that AD =  [#permalink]

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18 Jul 2018, 00:09
ABC is an equilateral triangle with point D on line BC such that AD = 4 units. What is the area of triangle ABC in square units?

Look at the attached figure. In $$\triangle{ADB}$$, we know one side and one angle thus the triangle can be of any size. so if we know ANY angle or ANY side, we can find all the sides as the triangle will be unique

(1) AD is perpendicular to BC.
If AD is perpendicular, AD is altitude and we can find sides and thus area of triangle
AD=4=$$side*\sqrt{3}/2$$
you can find side and thus area..
suff

(2) D is mid point of BC.
D is a midpoint means it is also perpendicular bisector
same as above
suff

D
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Re: ABC is an equilateral triangle with point D on line BC such that AD = &nbs [#permalink] 18 Jul 2018, 00:09
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# ABC is an equilateral triangle with point D on line BC such that AD =

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