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

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Math Expert
Joined: 02 Sep 2009
Posts: 60779
If the lengths of the sides of a triangle are a, b, and 7, which of  [#permalink]

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24 Mar 2019, 20:59
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If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a – b ?

I. 4
II. 7
III. 12

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

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24 Mar 2019, 21:14
2
As per the Third Side Rule of triangles: the third side of a triangle must always be less than the sum of the other two sides, and greater than the difference.
so here a-b<7
So OA:(A)
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Re: If the lengths of the sides of a triangle are a, b, and 7, which of  [#permalink]

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24 Mar 2019, 21:19
Bunuel wrote:
If the lengths of the sides of a triangle are a, b, and 7, which of the following could be the value of a – b ?

I. 4
II. 7
III. 12

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

third side rule ; a+b>7
so a,b can be 6,1 or 11,7 difference = 4

for a-b=7 ; the value a,b has to be 14 ; a,b 8,1 ; 9,2 , 10,3 not possible
a-b= 12; a,b can be 14,2 , 15,3 value of third side ; 2,3 will be too short to meet and connect with 7

IMO A
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Re: If the lengths of the sides of a triangle are a, b, and 7, which of  [#permalink]

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22 Nov 2019, 00:20
Standard triangle properties,

a-b < 7 < a+b

Only 4 is less than 7 among the options.

Ans A
Re: If the lengths of the sides of a triangle are a, b, and 7, which of   [#permalink] 22 Nov 2019, 00:20
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