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Three sides of an acute angled triangle are 10, 6 and k

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Carcass
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Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   05 May 2023, 07:31
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Three sides of an acute angled triangle are 10, 6 and k


Quantity A
Quantity B
\(k\)
\(12\)




A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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B
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Midhilesh489
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Re: Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   05 May 2023, 08:00
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Acute angled triangle property A^2 < B^2 + C^2 where is A is longest side

Sides can be taking only >= 12 which satisfies triangle property

10 6 12
10 6 13
10 6 14
10 6 15

12^2 > 10^2 + 6^2

So for k >= 12 there is no value which satisfies the property so K < 12 ( 10 6 11, 10 6 10, 10 6 9 ... satisfies)

Option B
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Re: Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   15 Jul 2024, 02:58
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According to TSR(k) (Third side rule of a triangle) of a triangle we have

10-6<k<10+6 =4<k<16

K can take any value between 4 and 16 to form 3-sided closed triangle.

But the question asks acute so it must be as less as possible and can take the value 5. so yes B>A
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Re: Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   21 Jul 2024, 08:46
Could someone please, explain this question? Carcass

we don't know if 10 is the longest side or not so, how can we prove that last side (k) would be exactly 12
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Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   21 Jul 2024, 08:51
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OE

As the triangle is an acute angled triangle so all the angles will be less than 90°. Now as we are comparing k with a constant value 12, means. k will be having a limiting value.

So, assuming if the triangle had been a right-angled triangle, with k being the longest side.

Attachment:
GRE triangle (13).jpg
GRE triangle (13).jpg [ 17.75 KiB | Viewed 686 times ]


\(k^2=6^2+10^2\)

\(K=\sqrt{136} = 11.66 \approx \)

Therefore, maximum possible value of k is 11.66, which is less than 12.
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Re: Three sides of an acute angled triangle are 10, 6 and k [#permalink] New post   26 Oct 2024, 17:45
For acute angled triangle each angle <90 and square any side is less than the sum of square of the other two sides
eg.

BC^2 < AB^2 + AC^2

therefore
the max value of K^2 < (10^2) + (6^2)
=> K^2 < 100 + 36
=> K^2 < 136
=> K< 12

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Option B
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gmatclubot
Re: Three sides of an acute angled triangle are 10, 6 and k [#permalink]
26 Oct 2024, 17:45
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