In right triangle ABC above, the length of AB is 5*3^1/2. What is the

Question

https://gmatclub.com/forum/download/file.php?id=26644 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. Kudos for a correct solution . 2015-05-13_1533.png

Bunuel · Accepted Answer

OFFICIAL SOLUTION:

https://gmatclub.com/forum/download/file.php?id=26644 
 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.

NavenRk · Answer

A Since DBC is an equilateral triangle , ADB = DCB + DBC =120
 ABD = 90- DBC = 30. Hence ADB is isoceles with ABD=DAB = 30.

The sides BC,CD,AD & DB are all equal.

Let BC=x => AC=2x

In rt triangle ABC  AC^2=AB^2+BC^2.

ie  (2x)^2  =  x^2 + (5\sqrt{3})^2 
x=5. Hence area of ABC=  25\sqrt{3} / 2

A is sufficient

B is insufficient

lipsi18 · Answer

AB=5root3, ABC is right angle triangle. Therefore area of ABC = 5root3 *BC/2; hence if we get value of BC we can answer the question.

1. BCD is equilateral, we know BD=BC=DC; but we don't know the value; insufficient
2. ABD is isosceles, we know AD=BD; definitely not sufficient

1+2 we know AD=BD=BC=DC but we still don't know the value, insufficient

Hence answer is E

Thanks,

EMPOWERgmatRichC · Answer

Hi lipsi18,

When dealing with DS questions, you sometimes have to take your thought process a little "farther" than you think you need to.

In this question, we're asked to find the area of the large right triangle. We're given the length of one of the legs, so we need to know the length of the other leg.

In Fact 1, we're told that BCD is equilateral. You correctly deduced that BD=BC=DC, but then it looks like you stopped working. Since all 3 sides of that triangle are equal, what does that mean about all 3 ANGLES in that triangle? So what does that make angle C? By extension, can you now figure out the length of the other leg of the right triangle? Fact 1 is actually SUFFICIENT and I think you already know everything that you need to know to prove it....you just didn't do enough work.

That last bit is important because DS questions have no "safety net" - if you miss a detail, make a little mistake or don't do enough work, then you're probably going to get the question wrong and not even know it.

GMAT assassins aren't born, they're made,
Rich

D3N0 · Answer

Ans: A
Solution: we know the length of AB now to get the Area we need height of the triangle.
1) from statement 1 we know that as triangle DBC is equilateral triangle,it means angle BCA is 60 and angle ABC is 90 so BAC is 30.
now we can find the lenght of BC and hence Area of the Triangle ABC

2) From statement 2 we know ABD is isosceles triangle.   we can't say which two arms are equal.
still even if we know that which two arms we can not get the Area of Triangle ABC.

Ans: A (statement 1 alone sufficient to answer the question)

ApurbaGMAT · Answer

We know the length of AB. In order to find the area of triangle ABC, easiest way is to  find the side BC .

1)  From Statement 1:  We know that DBC is an equilateral triangle, from this we can find all the interior angles of triangle ABC as well. If one acute angle of a right angled triangle and one side is known, we can find the other sides (Trignometry). ie. in this case  BC  -

2)  From Statement 2:  We know ABD is isosceles triangle, but we can't say which two arms are equal and through this we can't find side BC or any other side. Eventually we can't deduce the area of triangle ABC.

Answer:  A

23a2012 · Answer

the answer is A 
from the stem we know that angle B=90 and statment 1 said that tringle DBC is equilateral triangle so angle ABD=30 ,angle C=60, angle BDC=60 which lead to angle A=30 and angle ADB=120 as the result we have angle ABD=angle DAB so tringle ADB is isosceles triangle
in tringle ABC BC=X, AB=Xsqr3, AC=2X SO as BC is the basic =5, AB=is the hight = 5 Square root 3 then the area is (25 Square root3)/2

statment 2 insuff were we know from statment 1 that tringle ADB is isosceles triangle

rohitkumar77 · Answer

A is sufficient enough ; if you know bdc is equi - then we can simply use the 30-60-90 rule

@bunnel : When we have an option in DS that says " TRIANGLE ABC IS ISOSCELES " do we take that AB = BC or not ; 
only this statement is given " TRIANGLE ABC IS ISOSCELES "

In gmat i hope it would be specified which sides are isosceles

AdiBir · Answer

Given:  
ABC is a right triangle and AB =  5\sqrt{3} .

To Find:  
Area of ABC.

Pre-Process:  
We are already given AB(consider it as height of triangle) and we need one to find one more side to get the area.
 A = \frac{1}{2}*AB*BC 
We need to find BC somehow.

Now coming to the statements:

1)  says DBC is equilateral triangle. So each angle in DBC is 60. 
That tells us that the other angle of ABC is 30. 
We can find BC easily using the  1:\sqrt{3}:2  rule.
So statement  1)  is   sufficient  .

2)  says ABD is an isosceles triangle. 
But we don't know which two sides are equal.
  Not Sufficient  .

Hence  A  is the answer.

Hit Kudos if you like the explanation.

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In right triangle ABC above, the length of AB is 5*3^1/2. What is the

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