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Re: What is the maximum possible area of triangle? [#permalink]

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21 May 2012, 23:17

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

My answer would be E.

1. Two sides are 7 and 14 but we don't know which is base and which is height. Third side is 7< x < 21. 2. We are only given one side and no info whether this is B or H.

Re: What is the maximum possible area of triangle? [#permalink]

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22 May 2012, 06:18

I think answer is A.

Two sides are 7 an 14 so by the triangle sides property third side can be in between of 7 and 21. We need to maximise the area of triangle which is possible with these two sides and another sides so we will choose the third side as 20 (Assumption is sides are integer). Triangle with sides 7 ,14 and 20 will have the max area and this can be calculate using the below formula.

Re: What is the maximum possible area of triangle? [#permalink]

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22 May 2012, 20:59

To maximize the area of a triangle and if you know the length of two sides make them perpendicular to maximize the area. Hence A is sufficient. However, I do have my doubts about this answer as well.. where are the experts?

Re: What is the maximum possible area of triangle? [#permalink]

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22 May 2012, 21:19

1

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Smita04 wrote:

Bunuel, can you please comment on this? Is it not a GMAT type question? If that is the case, then there is no point discussing it.

Hi Smita04,

This is very much a GMAT query.

Evaluating statement 1 only: Here, we know that the length of the two sides are 7 cms and 14 cms respectively. Now just picture this. Let us try to a triangle with base = 14 cm and then try to put the 7 cm side such that ther area is the maximum.

Let the side AB = 7 cm and BC = 14 cm. The figure shows 3 possibilities for AB that would result in the maximum possible area for triangle ABC. Now, we k now that area = 1/2 * base * altitude = 1/2 * BC * altitude. Now, the area will be maximum for the maximum value of the altitude. This is only possible with AB as the altitude, as in the other two cases the length of the altutide goes down. Hence, ABC is right angled and the maximum area = 1/2 * 14 * 7 We can eliminate options B, C and E.

Evaluating statement 2 only: Let us picture this.

Let side AB = 7 cm. Now depending on the size of the circle, the area of the triangle can keep increasing. Hence, statement 2 alone is insufficient. Hence D is eliminated. Answer is A.

Re: What is the maximum possible area of triangle? [#permalink]

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06 Jun 2012, 12:36

what is OA smita? i got E as i thought it is not possible to find are untill we know which side is given what? can someone explain what is regarding maximising sides?

Re: What is the maximum possible area of triangle? [#permalink]

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10 Oct 2012, 02:08

1

This post received KUDOS

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A
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Re: What is the maximum possible area of triangle? [#permalink]

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10 Oct 2012, 08:28

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fameatop wrote:

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A

(1) You are absolutely right. Since only two sides of the triangle are given, the area varies depending on the third side. Since we can make the area as small as we wish and the third side must be between 7 and 21, the area must be finite for every one of these possible triangles. So, there must be a maximum, and because this is a DS question, we are not supposed to find that maximum. Trigonometry is out of question on the GMAT, but even without it, we can figure out when the area is maximum.

Since the area of a triangle is the same regardless which side we take as a base, we can consider 14 (denoted by BC in the attached drawing) as a constant base, and look at the various triangles that can be formed. Angle ABC varies between 0 and 180, with the side AC of constant length 7. Maximum height corresponding to BC is obtained when AB is perpendicular to BC, and in fact we now know that the maximum area will be 14*7/2 = 49. Indeed (1) is sufficient.

(2) Any triangle can be inscribed in a circle and through two given points (apart at a distance of 7) there are infinitely many circles passing through. Obviously not sufficient.

Hence answer A.

Attachments

TriangleMaxArea.jpg [ 9.9 KiB | Viewed 19234 times ]

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Re: What is the maximum possible area of triangle? [#permalink]

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31 May 2016, 22:02

EvaJager wrote:

fameatop wrote:

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

Good question. I feel this can be perfect GMAT question.

Q ->What is the maximum possible area of triangle ? 1) Let the third side is x which ranges from 7<x<21 where x can take any value within this range.

Now the three sides of the triangle are 7, 14, 7<x<21. Using these 3 sides numerous triangles can be made but only 1 triangle will have the maximum area , which we can find out (but it is not required to find the max area) Sufficient

2) Outright insufficient

Answer A

(1) You are absolutely right. Since only two sides of the triangle are given, the area varies depending on the third side. Since we can make the area as small as we wish and the third side must be between 7 and 21, the area must be finite for every one of these possible triangles. So, there must be a maximum, and because this is a DS question, we are not supposed to find that maximum. Trigonometry is out of question on the GMAT, but even without it, we can figure out when the area is maximum.

Since the area of a triangle is the same regardless which side we take as a base, we can consider 14 (denoted by BC in the attached drawing) as a constant base, and look at the various triangles that can be formed. Angle ABC varies between 0 and 180, with the side AC of constant length 7. Maximum height corresponding to BC is obtained when AB is perpendicular to BC, and in fact we now know that the maximum area will be 14*7/2 = 49. Indeed (1) is sufficient.

(2) Any triangle can be inscribed in a circle and through two given points (apart at a distance of 7) there are infinitely many circles passing through. Obviously not sufficient.

Hence answer A.

Statement 2 > Among all triangles inscribed in a given circle, the equilateral one has the largest area.

So if we consider side as 7, we can get the maximum area. Note that, question is asking for maximum area, not exact area. I think OA should Be D.

Re: What is the maximum possible area of triangle? [#permalink]

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07 Sep 2017, 23:38

Smita04 wrote:

What is the maximum possible area of triangle?

(1) Two sides of the triangle are 7 cm and 14 cm. (2) The triangle is inscribed in a circle and one of its sides is 7 cm.

ohhh okay I see what this question is doing

So to maximize the area of a triangle you would make it perpendicular- and although we don't know the third side of the triangle it we make it perpendicular it cannot be greater than 21 because 7 +14 must be greater than 21- so eitherway this is actually sufficient