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The 3 sides of an isosceles triangle are 6,a and b(in cm), out of whic

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The 3 sides of an isosceles triangle are 6,a and b(in cm), out of whic  [#permalink]

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New post 04 Mar 2019, 11:02
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The 3 sides of an isosceles triangle are 6,a and b(in cm), out of which 2 are equal. If a and b are integers, what is the value of the unequal side?

I. Sum of and b is a prime number less than 10cm.
II. the perimeter of the triangle is 13cm.
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Re: The 3 sides of an isosceles triangle are 6,a and b(in cm), out of whic  [#permalink]

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New post 04 Mar 2019, 12:25
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kiran120680 wrote:
The 3 sides of an isosceles triangle are 6,a and b(in cm), out of which 2 are equal. If a and b are integers, what is the value of the unequal side?

I. Sum of and b is a prime number less than 10cm.
II. the perimeter of the triangle is 13cm.


The minimum sum of a and b has to be 7 (sum of lengths of two sides>3rd side)
Also either a=b with 6 being the unequal side, or one out of a and b is 6, and the other is the different side.

I-
a+b is a prime number less than 10 (and also >=7)
only 1 pair satisfies the condition- 6 and 1 (also note a and b are integers, so we cannot have a=b=3.5)
==>unequal side=1
Sufficient.

II-
perimeter=13
6+a+b=13
a+b=7
this reduces to statement I condition
Sufficient

Both statements are individually sufficient

Ans:D
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Re: The 3 sides of an isosceles triangle are 6,a and b(in cm), out of whic   [#permalink] 04 Mar 2019, 12:25
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