What is the area of triangular region ABC above?

What is the area of triangular region ABC above?

The area of triangle ABC = \(\frac{BD*AC}{2}\)

(1) The product of BD and AC is 20. The area of triangle ABC = \(\frac{BD*AC}{2}=\frac{20}{2}=10\). Sufficient.
(2) x = 45. No lengths of any line segment is known. Not sufficient.

Answer: A.
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What is the area of triangular region ABC above?

(1) The product of BD and AC is 20.
(2) x = 45

Case A:
BD is right-angled to AC (Given) in diagram, BD is height and AC is base of the triangle. Area can be calculated by 1/2* base X height. So, Sufficient.
Option C,E are eliminated.

Case B:
x = 45. Angle is not sufficient to find the area. This case is in-sufficient.
B is eliminated.

Answer choice is A.

1) area of triangle is half of the (base times altitude). which is 10. sufficient.
2) we are only given info on the the left portion divided by the altitude. the other portion area could be equal to the left portion or could be really elongated or small. can't tell. so not sufficient.

How can we know for sure that AD = DC or that AB=AC? This information is required for (1) to be sufficient and A to the correct answer.

If we look at the diagram they look equal but their is no proof in the information...

DO we assume in the GMAT that if the lines look equal they are equal? I always though this was a 'no no'

Area of a triangle = 1/2 * base * height, and here the base is AC, while the height is BD.

Statement 1 tells us the product of the base and height, i.e. BD*AC = 20.
Since the question is asking about the area, we know that the area is 1/2 the product of BD and AC.
With this statement, we do NOT know for sure that AD = DC / AB = AC / the lines are equal... frankly we don't need to know for this statement to be sufficient. We have the product of BD and AC, and given that the area is half of the product, we have enough information to answer the question.

Statement 2 (that angle BAC, x, is 45 degrees) implies that ABC is isoceles (AB=BC), but this is NOT enough to give us any idea (on its own) about AC or BD. Hence this statement is insufficient and A is the answer.

Hope this helps.

Area of a triangle = 1/2 * Base * Height ( product of BD and AC is known so the area is 10)
X=45 doesn't help to find out anything about the area.

Answer : A

Cheers !
Dhiraj

Bunuel, I understand that the statement 2 is insufficient. However, if there is a given number for AB side. Would the statement2 be sufficient to answer the question. Thanks in advance

No. Even in this case we wouldn't know much about triangle BDC. Notice that we don;t know whether AB = BC.
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Hi All,

We're asked to figure out the area of triangular region ABC above. For that, we'll need the Area formula:

Area = (1/2)(Base)(Height)

So to answer this question, we either need the base and height of triangle ABC or we need the areas of the two smaller triangles.

(1) The product of BD and AC is 20.

Fact 1 tells us that the product of the height (BD) and the base (AC) = 20, so all we have to do is multiply that by 1/2 to get the area.... (1/2)(20) = 10
Fact 1 is SUFFICIENT

2) X = 45

This Fact tells us NOTHING about any of the side lengths, so there's no way to determine the area.
Fact 2 is INSUFFICIENT

Final Answer:

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

i have 2 questions in my mind
1) does that angle shown indicates angle BDC is right angle for sure?
2) If yes then wouldn't it give us the properties of similar traingles where 45:45:90 degree ratio formulae will be applied. so does it means knowing any sides actual length will give us area of traingle from statement 2??

Hi santoshkhatri,

When working on a DS question, we CANNOT assume that the picture is 'drawn to scale', but we CAN assume that lines are straight and that numbers are accurate. In this drawing, we know that angle BDC is a right angle, so that means that angle BDA is also a right angle.

With the additional information in Fact 2, we know that triangle BDA is a 45/45/90, but we do NOT know what type of right triangle BDC is (we only know that one of the angles is 90 degrees, but we don't know either of the other two angles). If we knew any side of the 45/45/90, then we could determine the height of the larger triangle (re: ABC), but we still would not know the overall base of that triangle.

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

Asked: What is the area of triangular region ABC above?
Area of triangle ABC = BD * AC /2

(1) The product of BD and AC is 20.
Area of triangle ABC = BD * AC /2
=20/2 = 10
SUFFICIENT

(2) x = 45
Since no lengths are provided
NOT SUFFICIENT

IMO A

Solution:

Question Stem Analysis:

We need to determine the area of triangle ABC. Notice that AC is the base and the BD is the height of the triangle, therefore the area of triangle ABC is ½ x AC x BD.

Statement One Alone:

Since we are given that AC x BD = 20, the area of triangle ABC is ½ x 20 = 10. Statement one alone is sufficient.


Statement Two Alone:

Knowing angle A is 45 degrees does not allow us to determine the area of triangle ABC. Statement two is not sufficient.

Answer: A
_________________

From (1) --> Area ABC = 1/2 BD*AC --> Sufficient
From (2) --> No info to find the area
--> Answer: A

Answer: Option A

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chetan2u BrentGMATPrepNow

Per statement two, x= 45. As angle BDC is 90, angle BDA should be 90, so angle BDA is 45.

My query:
Can't we use the property of the 45:45:90 triangle to find out the measurement of the sides?

Hi sjuniv32,

When working on a DS question, we CANNOT assume that the picture is 'drawn to scale', but we CAN assume that lines are straight and that numbers are accurate. In this drawing, we know that angle BDC is a right angle, so that means that angle BDA is also a right angle.

With the additional information in Fact 2, we know that triangle BDA is a 45/45/90, but we do NOT know what type of right triangle BDC is (we only know that one of the angles is 90 degrees, but we don't know either of the other two angles). In addition, we do NOT know ANY of the actual side lengths - so there's no way to calculate the actual area of any part of that shape. If we knew any side of the 45/45/90, then we could determine the height of the larger triangle (re: ABC), but we still would not know the overall base of that triangle.

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

sjuniv32

Even for knowing sides of ABD, we require any of the three sides.

Now, knowing one side of ABD will still not help us as we are not aware of angles CBD or DCB.

So, to answer this through statement 2, we require
1) Any of the sides of ABD
2) Any of the two sides apart from BD of BCD,
OR
Any of the two angles CBD or DCB
_________________

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