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what is the area of the triangle ABC? [#permalink]
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07 Mar 2018, 08:20
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What is the area of the triangle ABC? (1) The sides AB and BC are in ratio 1:2 while the sum of sides AB and BC is 60. (2) The angle BAC = 120 deg.
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Re: what is the area of the triangle ABC? [#permalink]
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07 Mar 2018, 09:17
When you combine the info, there is only ONE possible triangle... AB =20 and BC =40... Draw a line with one end as A.. Make a 120° angle from A and cut 20 units on that line as B.. From B take 40 units on a line, it will cut the line starting with A at one end at a point C.. Since you have a unique triangle, you can find Area.. Sufficient C Posted from my mobile device
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Re: what is the area of the triangle ABC? [#permalink]
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07 Mar 2018, 09:30
gmatbusters wrote: What is the area of the triangle ABC?
(1) The sides AB and BC are in ratio 1:2 while the sum of sides AB and BC is 60. (2) The angle BAC = 120 deg. Imo C From statement 1 we can not calculate area as we are not given the third side . We can calculate the individual values of the two sides but that is unhelpful as we need third side for area using heron's formula. From 2 We know the measure of every angle but we dont know the sides so insufficient Together they are sufficient as we know two sides and it is and isosceles triangle so we we draw perpendicular from A and calculate the altitude using 306090 triangle
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Re: what is the area of the triangle ABC? [#permalink]
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07 Mar 2018, 09:54
How you got it isosceles? arvind910619 wrote: gmatbusters wrote: What is the area of the triangle ABC?
(1) The sides AB and BC are in ratio 1:2 while the sum of sides AB and BC is 60. (2) The angle BAC = 120 deg. Imo C From statement 1 we can not calculate area as we are not given the third side . We can calculate the individual values of the two sides but that is unhelpful as we need third side for area using heron's formula. From 2 We know the measure of every angle but we dont know the sides so insufficient Together they are sufficient as we know two sides and it is and isosceles triangle so we we draw perpendicular from A and calculate the altitude using 306090 triangle
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Re: what is the area of the triangle ABC? [#permalink]
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09 Mar 2018, 08:12
Standard formula : area of any triangle = (1/2) a*b* Sin(included angle (a,b)).
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what is the area of the triangle ABC? [#permalink]
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Updated on: 09 Mar 2018, 08:31
Hi Guys Whenever any DS question asks about Area, Perimeter or any other details related to a triangle, we should visualize if the triangle can be uniquely drawn or not.This Question is based on a very NOTE IMPORTANT EXCEPTION:The SSA condition (SideSideAngle) which specifies two sides and a nonincluded angle (also known as ASS, or AngleSideSide) does not always prove congruence, even when the equal angles are opposite equal sides. Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In all other cases with corresponding equalities, SSA proves congruence. The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (HypotenuseLeg) condition or the RHS (RightangleHypotenuseSide) condition), we can calculate the third side and fall back on SSS. If any triangle follows laws of Congruency, it means it can be drawn Uniquely.Happy Learning
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Originally posted by gmatbusters on 09 Mar 2018, 08:28.
Last edited by gmatbusters on 09 Mar 2018, 08:31, edited 1 time in total.



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Re: what is the area of the triangle ABC? [#permalink]
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09 Mar 2018, 08:29
please read the second statement carefully, the angle given is not the included angle. srinjoy1990 wrote: Standard formula : area of any triangle = (1/2) a*b* Sin(included angle (a,b)).
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Re: what is the area of the triangle ABC? [#permalink]
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09 Mar 2018, 08:46
Now the Question arises, why the SSA congruency rule is valid for obtuse and right angled triangle, but not for acuteangled triangle. It can be easily seen through the attached sketch, how the right angle and obtuse angle define the triangle clearly. gmatbusters wrote: Hi Guys
Whenever any DS question asks about Area, Perimeter or any other details related to a triangle, we should visualize if the triangle can be uniquely drawn or not.
This Question is based on a very NOTE IMPORTANT EXCEPTION:
The SSA condition (SideSideAngle) which specifies two sides and a nonincluded angle (also known as ASS, or AngleSideSide) does not always prove congruence, even when the equal angles are opposite equal sides.
Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In all other cases with corresponding equalities, SSA proves congruence.
The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (HypotenuseLeg) condition or the RHS (RightangleHypotenuseSide) condition), we can calculate the third side and fall back on SSS.
If any triangle follows laws of Congruency, it means it can be drawn Uniquely.
Happy Learning
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WhatsApp Image 20180309 at 21.13.07.jpeg [ 109.55 KiB  Viewed 713 times ]
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Re: what is the area of the triangle ABC? [#permalink]
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12 Mar 2018, 13:22
gmatbusters wrote: What is the area of the triangle ABC?
(1) The sides AB and BC are in ratio 1:2 while the sum of sides AB and BC is 60. (2) The angle BAC = 120 deg. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. We suppose a triangle has 3 variables, since we can determine a triangle, if we know 3 lengths of the triangle's sides. Since we have 2 equations from the condition 1 which are \(AB:BC = 1:2\) and \(AB + BC = 60\) and 1 equation from the condition 2), both conditions together 1) & 2) are sufficient. We have \(AB = 20\) and \(BC = 40\) from the condition 1) The area of the triangle is \(\frac{1}{2} \cdot AB \cdot BC \cdot sin(120°) = \frac{1}{4} \cdot 20 \cdot 40 \cdot \sqrt{3} = 200\sqrt{3}\) Therefore, the answer is C.
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Re: what is the area of the triangle ABC? [#permalink]
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13 Mar 2018, 06:10
Hii I am afraid, your approach doesn't seem right. In the formula, A = (Side1 * Side2 * Sin Angle)/2, the angle should be the included angle. MathRevolution wrote: gmatbusters wrote: What is the area of the triangle ABC?
(1) The sides AB and BC are in ratio 1:2 while the sum of sides AB and BC is 60. (2) The angle BAC = 120 deg. Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. We suppose a triangle has 3 variables, since we can determine a triangle, if we know 3 lengths of the triangle's sides. Since we have 2 equations from the condition 1 which are \(AB:BC = 1:2\) and \(AB + BC = 60\) and 1 equation from the condition 2), both conditions together 1) & 2) are sufficient. We have \(AB = 20\) and \(BC = 40\) from the condition 1) The area of the triangle is \(\frac{1}{2} \cdot AB \cdot BC \cdot sin(120°) = \frac{1}{4} \cdot 20 \cdot 40 \cdot \sqrt{3} = 200\sqrt{3}\) Therefore, the answer is C.
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Re: what is the area of the triangle ABC? [#permalink]
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13 Mar 2018, 06:33
pushpitkc niks18 Hatakekakashiamanvermagmat BunuelAny way to link opposite sides with angles here since ratio between sides is given? If AB = x, BC = 2x and AB + BC = 60. We can get AB = 20 and BC = 40. How do I get third side length here?
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what is the area of the triangle ABC? [#permalink]
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13 Mar 2018, 07:14
adkikaniPlease see the explanation below, we can very easily find the third side by constructing the triangle. BINGO!!!, actually u need not draw the triangle to the scale, but yes u can see that you can draw, So the triangle can be uniquely drawn. Hence all parameter related to tank can be found out. You might also like this question: https://gmatclub.com/forum/whatisthe ... l#p2027579Happy Learning!!! gmatbusters wrote: Now the Question arises, why the SSA congruency rule is valid for obtuse and right angled triangle, but not for acuteangled triangle. It can be easily seen through the attached sketch, how the right angle and obtuse angle define the triangle clearly. gmatbusters wrote: Hi Guys
Whenever any DS question asks about Area, Perimeter or any other details related to a triangle, we should visualize if the triangle can be uniquely drawn or not.
This Question is based on a very NOTE IMPORTANT EXCEPTION:
The SSA condition (SideSideAngle) which specifies two sides and a nonincluded angle (also known as ASS, or AngleSideSide) does not always prove congruence, even when the equal angles are opposite equal sides.
Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In all other cases with corresponding equalities, SSA proves congruence.
The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (HypotenuseLeg) condition or the RHS (RightangleHypotenuseSide) condition), we can calculate the third side and fall back on SSS.
If any triangle follows laws of Congruency, it means it can be drawn Uniquely.
Happy Learning
Attachments
WhatsApp Image 20180309 at 21.13.07 (1).jpeg [ 109.55 KiB  Viewed 492 times ]
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what is the area of the triangle ABC? [#permalink]
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13 Mar 2018, 12:25
adkikani wrote: pushpitkc niks18 Hatakekakashiamanvermagmat BunuelAny way to link opposite sides with angles here since ratio between sides is given? If AB = x, BC = 2x and AB + BC = 60. We can get AB = 20 and BC = 40. How do I get third side length here? Hi adkikaniIn GMAT triangle area question we generally need to know the base and height of the triangle. In this question you can extend the base AC to the point D and then draw a perpendicular from C to D to get the height CD. Refer below figure for detailed solution  Attachment:
Triangle.jpg [ 47.24 KiB  Viewed 457 times ]



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Re: what is the area of the triangle ABC? [#permalink]
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13 Mar 2018, 12:48
adkikani wrote: pushpitkc niks18 Hatakekakashiamanvermagmat BunuelAny way to link opposite sides with angles here since ratio between sides is given? If AB = x, BC = 2x and AB + BC = 60. We can get AB = 20 and BC = 40. How do I get third side length here? brilliant explanation by niks18




Re: what is the area of the triangle ABC?
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