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# One side of a triangle has length 8 and a second side has length 5. Wh

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Math Expert
Joined: 02 Sep 2009
Posts: 64101
One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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17 May 2016, 02:42
3
13
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Difficulty:

75% (hard)

Question Stats:

37% (01:19) correct 63% (02:17) wrong based on 141 sessions

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One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?

I. 24
II. 20
III. 5

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

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Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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17 May 2016, 09:43
4
2
The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 8 and 5 are the base and height of triangle .
Area = 1/2 * 8 * 5 = 20
There is no lower limit on the area of any triangle whose only 2 sides are known . Area> 0
So we can also have triangle with area = 5

Suppose we want to take 8 as the hypotenuse in the right angled triangle , then one of the other sides(base or height) will be less than 8 .
Hence , product will be lesser than 20 .

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Joined: 06 Feb 2016
Posts: 12
Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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17 May 2016, 10:06
1
I agree D too. Taking it that the 2 possible largest sides to calculate area of triangle are 5 and 8 then (8x5/2 = 20).

One could also try the validity of 5 by assuming that 8 is the hypothenuse so a^2 +b^2 = c^2 would look something like a^2+5^2 = 8^2 and thus a must be an estimate of 6~ assuming we use 6 then 6*5=30/2 = 15 and thus assuming that any answer below 20 is possible is correct!
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Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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08 Sep 2016, 20:39
1
Hello Friends,
Initially, i wasn't sure as to how we can get 3rd side = 2.
Because, |8-5| < 3rd side < |8+5| => 3 < 3rd side < 13. Following image helped...
Now, as skywalker18 correctly mentioned max area of triangle is when it is right triangle.
So, we can't have 3rd side as >= 6 because if so we COULD get 6*8/2 = 24 [NOT POSSIBLE]
so, 3 < 3rd side < 6.

Still based on the diagram area of triange CAN be 5.
Attachments

File comment: If this help, please kudo...

3_rd_side_2.png [ 1.48 KiB | Viewed 8065 times ]

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Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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03 Nov 2016, 07:43
Hi manishtank1988
If the minimum length of the third side could be 4 then the minimum area is 1/2*4*5=10 which rules out the possibility of III. Could you elaborate it?
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Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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31 Jul 2018, 18:35
1
Area of a triangle is (1/2) * a*b*sin (angle between a and b)
Since sine has the max positive value 1 and minimum value 0 , hence the area of triangle could be anything between 0 and 20
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Re: One side of a triangle has length 8 and a second side has length 5. Wh  [#permalink]

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03 Aug 2019, 06:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: One side of a triangle has length 8 and a second side has length 5. Wh   [#permalink] 03 Aug 2019, 06:40