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# If 7 and 10 are the lengths of two sides of a triangle, which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
If 7 and 10 are the lengths of two sides of a triangle, which of the  [#permalink]

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21 Aug 2018, 20:48
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72% (00:30) correct 28% (00:32) wrong based on 47 sessions

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If 7 and 10 are the lengths of two sides of a triangle, which of the following can be the length of the third side?

I. 2
II. 8
III. 17

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

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Re: If 7 and 10 are the lengths of two sides of a triangle, which of the  [#permalink]

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21 Aug 2018, 20:54
The third side of triangle should be greater than the difference between the other two sides and less than the sum of the other two sides.

10-7 < x < 10+7

3 < x < 17

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If 7 and 10 are the lengths of two sides of a triangle, which of the  [#permalink]

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21 Aug 2018, 21:33
Bunuel wrote:
If 7 and 10 are the lengths of two sides of a triangle, which of the following can be the length of the third side?

I. 2
II. 8
III. 17

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

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, $$(10-7)<x<(10+7)$$
Or, $$3<x<17$$.
Hence 2 and 17 cannot be the length of the third side but 8 can be.

Ans.(A)
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Re: If 7 and 10 are the lengths of two sides of a triangle, which of the  [#permalink]

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21 Aug 2018, 21:58

Solution

Given:
• 7 and 10 are the lengths of two sides of a triangle.

To find:
• The possible length of the third side.

Approach and Working:
We know that for any triangle, the sum of any two sides is always greater than the third side.
Similarly, the difference of any two sides is always less than the third side.

So, if the length of the third side is T, then we can say
• 7 + 10 > T
Or, T < 17

• Similarly, 10 – 7 < T
Or, T > 3

Combining them, we can write 3 < T < 17

From the given choices, we can say T can only be 8.
Hence, the correct answer is option A.

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Re: If 7 and 10 are the lengths of two sides of a triangle, which of the   [#permalink] 21 Aug 2018, 21:58
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