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505-555 (Easy)|   Geometry|      
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Bunuel
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A triangle has a base of length 13 and the other two sides are equal 01 Sep 2017, 00:38
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88% (01:14) correct 12% (01:49) wrong based on 94 sessions

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A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

(A) 1
(B) 2
(C) 5
(D) 7
(E) 13
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D
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A triangle has a base of length 13 and the other two sides are equal 01 Sep 2017, 01:11
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D. Sum of any two sides is always greater than third side of a triangle. If we take 7, then 13+7>7 and 7+7>13.

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A triangle has a base of length 13 and the other two sides are equal 01 Sep 2017, 11:44
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Bunuel
A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

(A) 1
(B) 2
(C) 5
(D) 7
(E) 13
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If the sum of any two sides must be greater than the length of the third side, and equal other sides = x, then

2x > 13, and
x > 6.5

Answer E, 13, would work (an equilateral triangle is a special isosceles triangle), but we are asked for the shortest possible length of a side.

ANSWER D, 7, satisfies both conditions.
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A triangle has a base of length 13 and the other two sides are equal 02 Sep 2017, 06:14
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two sides are equal then we have
than from triangle property sum of two sides is grater than the third side and third side is greater than the difference of the two sides

13-x<x<13+x
13-x<x=13<2x
or 6.5<x
x is an inter therefore 7

Hence the answer is D
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A triangle has a base of length 13 and the other two sides are equal 02 Sep 2017, 07:18
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Bunuel
A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

(A) 1
(B) 2
(C) 5
(D) 7
(E) 13
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Sum of the 2 sides of the triangle should be greater than the 3rd side.
Consider a as the unknown side and being equal to the other unknown; a+a>13

2a>13.

The smallest integer satisfying the above condition is 7. Hence the answer D
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A triangle has a base of length 13 and the other two sides are equal 07 Sep 2017, 07:15
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Bunuel
A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?

(A) 1
(B) 2
(C) 5
(D) 7
(E) 13
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We see that we have an isosceles triangle. Since the sum of any two sides of a triangle has to be greater than the third, the shortest length of any side of an isosceles triangle when one side is 13 is 7, if that length has to be an integer. (Notice that 7 + 7 = 14 > 13. If the length were less than 7, say 6, then we would have 6 + 6 = 12, which is not greater than 13.)

Answer: D
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A triangle has a base of length 13 and the other two sides are equal 07 Sep 2017, 22:07
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As we know in triangle , sum of two sides should be greater than the third side.

Thus, the third side would be 7.

7+7 > 13 ( as 2 sides of triangle are equal )

Answer : D
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