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555-605 Level|   Geometry|      
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Bunuel
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Triangle ABC has sides of lengths 7, 13 and x, where x is the length 15 Aug 2017, 02:20
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C
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25% (medium)

Question Stats:

72% (01:27) correct 28% (01:43) wrong based on 73 sessions

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Triangle ABC has sides of lengths 7, 13 and x, where x is the length of the longest side. If x is the square of an integer, the perimeter of ∆ ABC is equal to which of the following?

(A) 24
(B) 29
(C) 36
(D) 45
(E) 49
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C
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prachi18oct
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Triangle ABC has sides of lengths 7, 13 and x, where x is the length 15 Aug 2017, 02:34
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C
Side 6<x <20
Perfect square can be 9 or 16
But x is longest so >13
Hence 16.
Perimeter 36.
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pushpitkc
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Triangle ABC has sides of lengths 7, 13 and x, where x is the length 15 Aug 2017, 02:47
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Bunuel
Triangle ABC has sides of lengths 7, 13 and x, where x is the length of the longest side. If x is the square of an integer, the perimeter of ∆ ABC is equal to which of the following?

(A) 24
(B) 29
(C) 36
(D) 45
(E) 49

The third side(x) which is a square of an integer can be 16 or 9
But a triangle with sides 7,9 and 13 cannot be possible x must be the larger side.
The perimeter could be 7+13+16 which is 36(Option C)
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Triangle ABC has sides of lengths 7, 13 and x, where x is the length 18 Aug 2017, 09:12
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Bunuel
Triangle ABC has sides of lengths 7, 13 and x, where x is the length of the longest side. If x is the square of an integer, the perimeter of ∆ ABC is equal to which of the following?

(A) 24
(B) 29
(C) 36
(D) 45
(E) 49

The perimeter of the triangle is 7 + 13 + x = 20 + x. Let’s analyze each answer choice.

A) 24

If the perimeter is 24, then:

20 + x = 24 → x = 4

Since 4 cannot be the longest side, answer A is not correct.

B) 29

If the perimeter is 29, then :

20 + x = 29 → x = 9

Since 9 cannot be the longest side, answer B is not correct.

C) 36

If the perimeter is 24, then:

20 + x = 36 → x = 16

Since 16 is a perfect square and it is larger than 7 and 13, 16 can be the longest side and 36 can be the perimeter.

Alternate Solution:

Since x is the longer side, x > 13. Furthermore, by the triangle inequality, x should be less than the sum of the other two sides; therefore x < 7 + 13 = 20. That is, 13 < x < 20. Looking for a perfect square integer between 13 and 20, we see that 16 is the only choice. Therefore, the perimeter of the triangle is 7 + 13 + 16 = 36.

Answer: C
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