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505-555 (Easy)|   Geometry|      
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Bunuel
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If 5 and 17 are the lengths of two sides of a triangular region, which 08 Oct 2021, 01:30
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15% (low)

Question Stats:

79% (00:42) correct 21% (00:50) wrong based on 66 sessions

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If 5 and 17 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 11
II. 13
III. 21

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II and III
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D
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If 5 and 17 are the lengths of two sides of a triangular region, which 08 Oct 2021, 01:51
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Bunuel
If 5 and 17 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 11
II. 13
III. 21

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II and III


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Solution:

We know a side property of triangle that the length of the 3rd side lies within the range:

Difference of 2 sides < 3rd side < Sum of 2 sides

Here we have 2 sides as \(5\) and \(17\).

So the range of 3rd side:

\(17-5<3^{rd} Side<17+5\)

\(12<3^{rd} Side<22\)

Looking at the options, we see that 13 and 21 comes in the range.

Hence the right answer is Option D.
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If 5 and 17 are the lengths of two sides of a triangular region, which 08 Oct 2021, 05:45
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Correct Option : D

The sides of a triangle rule asserts that
the sum of the lengths of any two sides of a triangle has to be greater than
the length of the third side.

I - 11 = 11+5 = 16 less than 3rd Side
II - 13 = 13+5 = 18 Greater than 3rd Side
III - 21 = 21+5 = 26 Greater than 3rd Side

II and III satisfy the condition - Option D
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If 5 and 17 are the lengths of two sides of a triangular region, which 08 Oct 2021, 09:22
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Bunuel
If 5 and 17 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 11
II. 13
III. 21

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II and III


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Difference in Length of 2 sides < Length of 3rd Side < Sum of 2 Sides

Or, ( 17 - 5 )< Length of 3rd Side < ( 17 + 5 )

Or, 12 < Length of 3rd Side < 22

Within the given range only option (D) comes, hence Answer must be (D)
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If 5 and 17 are the lengths of two sides of a triangular region, which 08 Oct 2021, 17:30
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in a triangle:
side 1 - side 2 < side 3 < side 1 + side 2
<=> 17 - 5 < side 3 < 17 + 5
<=> 12 < side 3 < 22

I. 11 => no
II. 13 => yes
III. 21 => yes

=> only II and III
=> D
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If 5 and 17 are the lengths of two sides of a triangular region, which 09 Oct 2021, 10:53
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IMO: D

Sum of any two sides of a triangle should be greater than third side.

With 11, third side is less than sum of other two sides. i.e. 5+11 < 17. So 11 cannot be the third side.

With 13 and 21, condition holds true for any pair of two sides.
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