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20 Jun 2015, 11:00
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In right triangle ABC above, the length of AB is \(5\sqrt{3}\). What is the area of triangle ABC?
(1) DBC is an equilateral triangle.
(2) ABD is an isosceles triangle:
20 Jun 2015, 11:00
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Official Solution:
In right triangle ABC above, the length of AB is \(5\sqrt{3}\). What is the area of triangle ABC?
(1) DBC is an equilateral triangle. This implies that each angle in DBC is 60°. So, angle C is also 60°. We know one side and all the angles in triangle ABC (90°-60°-30°). We can calculate anything we want about it. Sufficient.
(2) ABD is an isosceles triangle. We don't know which sides in ABD are equal, so more than 1 case is possible. Not sufficient.
Answer: A
In right triangle ABC above, the length of AB is \(5\sqrt{3}\). What is the area of triangle ABC?
(1) DBC is an equilateral triangle. This implies that each angle in DBC is 60°. So, angle C is also 60°. We know one side and all the angles in triangle ABC (90°-60°-30°). We can calculate anything we want about it. Sufficient.
(2) ABD is an isosceles triangle. We don't know which sides in ABD are equal, so more than 1 case is possible. Not sufficient.
Answer: A
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22 Jun 2015, 04:53
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Bunuel
Given
AB = 5 \sqrt{3} we need BC to find area
Statement 1,
DBC is an equilateral triangle.
Angle C = 60, hence Angle A = 30 so Triangle ABC is 30-60-90 triange
Hence Side opposite to 30 : Side opposite to 60 : Side opposite to 90 = 1 :\sqrt{3} : 2 = BC : AB : AC
But Side opposite to 60 = AB = 5 \sqrt{3}
Multiply whole ratio by 5 we get BC = 5
Sufficient to find area.
Statement 2 :
ABD is an isosceles triangle. But this wont help to find Angle A so clearly insufficient to find BC.
Hence Option A
