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One side of a triangle has length 6 and a second side has length 7.

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Bunuel
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One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   09 Aug 2017, 04:45
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One side of a triangle has length 6 and a second side has length 7. Which of the following could be the area of this triangle?

I. 13
II. 21
III. 24

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
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D
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chetan2u
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Re: One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   09 Aug 2017, 05:31
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Bunuel wrote:
One side of a triangle has length 6 and a second side has length 7. Which of the following could be the area of this triangle?

I. 13
II. 21
III. 24

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III


Hi...
Two points...
1. Area of triangle can be just slightly above 0 at the lower end.
2. The largest area will be right angle triangle with these sides

Ok lower end...Just above 0
Upper end... \(\frac{1}{2}*6*7=21\)
So 13 and 21 is possible, but 24 is NOT possible

D
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One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   09 Aug 2017, 15:26
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Nice one.
Here is what I did on this one -->


Side 1 -> 6
Side 2 -> 7

Maximum area would be when the two sides are perpendicular to each other forming a right triangle.

Hence Max. Area -> 1/2 * 6 * 7 => 21

Minimum area => When the third side would of length zero and the triangle would cease to exist.

Hence the range of Areas => [0,21]

Hence Option 1 and Option 2 are possible.
Option 3 is not.

Hence D.
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One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   09 Aug 2017, 18:52
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stonecold wrote:
Nice one.
Here is what I did on this one -->


Side 1 -> 6
Side 2 -> 7

Maximum area would be when the two sides are perpendicular to each other forming a right triangle.

Hence Max. Area -> 1/2 * 6 * 7 => 21

Minimumm area => When the third side would of length zero and the triangle would cease to exist.

Hence the range of Areas => [0,21]

Hence Option 1 and Option 2 are possible.
Option 3 is not.

Hence D.

stonecold, I was waiting for this comment so I could ask somebody, so thank you: are you talking about a degenerate triangle? The kind that looks like a line segment?

And if so, have you ever seen an official GMAT question that expects us to know that there is actually such a thing as a triangle with area of zero? :-D
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One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   09 Aug 2017, 21:04
Bunuel wrote:
One side of a triangle has length 6 and a second side has length 7. Which of the following could be the area of this triangle?

I. 13
II. 21
III. 24

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III


The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 6 and 7 are the base and height of triangle respectively or vice versa.
Max Area = 1/2 * 7 * 6 = 21
There is no lower limit on the area of any triangle whose only 2 sides are known. Hence 21 => Area > 0
So we can also have triangle with area = 13 but not with area 24
Hence D
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Re: One side of a triangle has length 6 and a second side has length 7. [#permalink] New post   05 Oct 2022, 04:45
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Re: One side of a triangle has length 6 and a second side has length 7. [#permalink]
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