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

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

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New post 17 May 2016, 03:42
3
6
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A
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D
E

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Question Stats:

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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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New post 17 May 2016, 10:43
2
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 .

Answer D
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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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New post 17 May 2016, 11:06
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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New post 08 Sep 2016, 21:39
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
3_rd_side_2.png [ 1.48 KiB | Viewed 4636 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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New post 03 Nov 2016, 08:43
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?
Thanks in advance.
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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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New post 31 Jul 2018, 19:35
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
Re: One side of a triangle has length 8 and a second side has length 5. Wh &nbs [#permalink] 31 Jul 2018, 19:35
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