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For a given triangle with sides x,3x and 24, what is the

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mau5
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For a given triangle with sides x,3x and 24, what is the [#permalink] New post   01 Aug 2013, 03:37
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For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   01 Aug 2013, 04:47
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Rule for triangles: the sum of two sides must be grater than the third side.

For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. \((x-3)(x-10) = 0\)
So x can be 3, and the sides would be \(3,9,24\) <== this is not a triangle as \(3+9<24\).
Or x can be 10, and the sides would be \(10,30,24\) <== this is a legit triangle.
Sufficient

II.The perimeter is a perfect square.
Applying the rule we get
\(3x+x>24\) or \(x>6\)
\(24+3x>x\) or \(12+2x>0\) (this is irrelevant as it's always true-x must be positive)
\(24+x>3x\) or \(12>x\). So \(12>x>6\) and the perimeter will range from
if \(x=12\), \(P=72\) - if \(x=6\) \(P=48\).
Between 48 and 72 there are the following perfect squares: \(49,64\). Thus x could have two values, and the perimeter would change.
Not sufficient
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   01 Aug 2013, 04:08
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

OA after some discussion.



From I X = 3 or X = 10, Plugging into stem- 3 + 9 + 24 = 36 or 10 + 30 + 24 = 64...not sufficient

From II...not enough info

I + II both potential answers are perfect squares, not sufficient..
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   03 Aug 2013, 08:08
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.


I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10
The answer is D.
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   03 Aug 2013, 08:16
bboev wrote:
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.


I is sufficient- it is clear
II x+3x+24=A*2
4x+24=A*2
4(X+6)=A*2
2*2 (X+6)= A*2
solution are x = 3, 10, 19, 30, 43...
for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle
x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10
x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19
x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30
So from II statement x is only 10
The answer is D.


You are assuming that x can only be an integer. you get a perfect square for \(x = \frac{25}{4}\) and forms a valid triangle.
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   03 Aug 2013, 08:23
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   03 Aug 2013, 08:28
AMITAGARWAL2 wrote:
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D


Nope.Please refer to the post above.

Thanks.
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   05 Aug 2013, 14:21
mau5 wrote:
AMITAGARWAL2 wrote:
i - sufficient. i think that is easy
ii - 24+x > 3X
So X < 12
and x+3x>24 then X > 6
24+4X perfect square x can only 10
Sufficient

So D


Nope.Please refer to the post above.

Thanks.


it's an obvious (A).
because x=3 or x=10 .
for a triangle with such sides (x,3x and 24) it's not possible that x=3. because x+3x>24 have to be true always). so x=10 and we know the perimeter = 4x+24=64
st(2) is not needed at all.
Answer is (A)
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   05 Jul 2018, 00:44
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mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.
#From first statement we have one value satisfying triangle's properties..ie x=10
*Strike out BCE. Ans must be A or D
*Now perimeter is 4x+24
#According to statement 2 it must b a perfect square...and because of traingles properties x must b greater than equals to 7 and less than 12(PROPERTY OF TRIANGLE I M TALKING ABOUT IS THAT SUM OF ANY TWO SIDES IS ALWAYS GREATER THAN THE THIRD ONE)
*4x+24= 64 is only condition in which x lies b/w 7 and 12(7 inclusive)
**SO ANS IS (D)
I ASSUMED THAT IS AN INTEGER


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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   05 Jul 2018, 01:01
mau5 wrote:
For a given triangle with sides x,3x and 24, what is the value of the perimeter?

I. (x-3)(x-10) = 0

II.The perimeter is a perfect square.

Source: My own.



sides x, 3x and 24
so
x+3x > 24
4x > 24
x > 6

1.x=3,x=10
since x is > 6 , x=10 sufficient

2. x+3x+24 = a^2
4x+24=perfect square
perfect squares > 24 are
36 for which 4x=12 , x =3
but x should be > 6
49 for which 4x=25 , x=6.25
64 for which 4x=30 , x=7.50
...
insufficient

A it is !!
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink] New post   14 Sep 2023, 10:46
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Re: For a given triangle with sides x,3x and 24, what is the [#permalink]
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