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Perimeter of an isosceles triangle

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Perimeter of an isosceles triangle

by gmattesttaker2 » Sat Feb 15, 2014 11:16 pm
Hello,

Can you please assist with this:

Two of the sides of an isosceles triangle measure 6 and 6 sq.root (3) , respectively, what
is its perimeter?

(1) One of the angles of the triangle is obtuse.
(2) The perimeter of the triangle is less than 24.

OA: D


Thanks,
Sri
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Source: — Data Sufficiency |
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by Patrick_GMATFix » Sat Feb 15, 2014 11:47 pm
"Obtuse" means greater than 90 degrees. I have never seen this vocabulary tested on an official question without its definition.

The known sides are 6 and 6root(3). Since the triangle is isosceles, the 3rd side must be 6 or 6root(3). Knowing which will allow us to find the perimeter.

Rephrase: Is the 3rd side 6 or 6root(3) ?

(1) Since the sum of angles in a triangle is 180, an obtuse angle (>90) must be the greatest angle (can't have 2 angles greater than 90). In any triangle, the largest angle will face the largest side,and two equal angles must face equal sides. We can deduce that this obtuse angle must face side 6root(3), and the other two sides must equal 6. Again, we cannot have two sides of length 6root(3) because we cannot have two obtuse angles in a triangle. Since we know the length of all sides, (1) is SUFFICIENT.

(2) root(3) is a bit more than 1.5 (memorize root(2)=1.4, root(3)=1.7). If the 3rd side had length 6root(3), the perimeter would be 2*6root(3)+6 which is a bit longer than 2*6*(3/2)+6 = 24. (2) tells us that the perimeter is less than 24, so the 3rd side must be 6. Since we know the length of all sides, (2) is SUFFICIENT.

Answer is D
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by gmattesttaker2 » Sun Feb 16, 2014 6:11 pm
Patrick_GMATFix wrote:"Obtuse" means greater than 90 degrees. I have never seen this vocabulary tested on an official question without its definition.

The known sides are 6 and 6root(3). Since the triangle is isosceles, the 3rd side must be 6 or 6root(3). Knowing which will allow us to find the perimeter.

Rephrase: Is the 3rd side 6 or 6root(3) ?

(1) Since the sum of angles in a triangle is 180, an obtuse angle (>90) must be the greatest angle (can't have 2 angles greater than 90). In any triangle, the largest angle will face the largest side,and two equal angles must face equal sides. We can deduce that this obtuse angle must face side 6root(3), and the other two sides must equal 6. Again, we cannot have two sides of length 6root(3) because we cannot have two obtuse angles in a triangle. Since we know the length of all sides, (1) is SUFFICIENT.

(2) root(3) is a bit more than 1.5 (memorize root(2)=1.4, root(3)=1.7). If the 3rd side had length 6root(3), the perimeter would be 2*6root(3)+6 which is a bit longer than 2*6*(3/2)+6 = 24. (2) tells us that the perimeter is less than 24, so the 3rd side must be 6. Since we know the length of all sides, (2) is SUFFICIENT.

Answer is D
Hello Patrick,

Thanks for your clear and detailed explanation and for all your help.

Best Regards,
Sri
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