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If the lengths of the sides of a triangle are 10, 20 and x, where x is

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Bunuel
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If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 01:16
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If the lengths of the sides of a triangle are 10, 20 and x, where x is a positive integer, how many values can x take?

A. 18
B. 19
C. 20
D. 21
E. 22
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B
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bmathur
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 01:33
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Since the third side of the triangle should be greater than the difference of the other two sides and smaller than the sum of the other two sides, we have 10<x<30. The smallest value x can take is 11 and the greatest is 29. Hence, we get 29 values. Answer is B.

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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 02:06
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We know the third side will be greater than the difference of other two sides and smaller than the sum of two side. i.e.

20-10 < x < 20+10
11 < x < 29 (we know, the value of 'x' is positive integer)

so, the total value from 11 to 29 (including) is 19

'B' is the Winner

Note: If the third side will be smaller than the difference of other two sides and greater than the sum of two side - it will not make a triangle
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 05:08
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diff of other two sides < value of third side < sum of other two side
20-10 < value of third side < 20+10
10<value of third side < 30

11,12,13,14..............29
total = 19

OA:B
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 05:10
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diff of other two sides < value of third side < sum of other two side
20-10 < value of third side < 20+10
10<value of third side < 30

11,12,13,14..............29
total = 19

OA:B
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 05:11
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diff of other two sides < value of third side < sum of other two side
20-10 < value of third side < 20+10
10<value of third side < 30

11,12,13,14..............29
total = 19

OA:B
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 05:32
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19 values as if the value of X is 1 to 9 the thrid side will be either short then the sum of other two sides or equal if 3rd side is 10. So 3rd side can take only 19 values

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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 05:32
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x should be between 10 and 30, so possible integer x is 11,12,...,29. There are 19 nos of possible integer value of x

FINAL ANSWER IS (B)

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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 10:17
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If the lengths of the sides of a triangle are 10, 20 and x, where x is a positive integer, how many values can x take?

A. 18
B. 19
C. 20
D. 21
E. 22

Maximum length possible would be Max(x) < 10 + 20 = 30
Minimum length possible would be Min(x) > 20 - 10 = 10

Possible values are as per 10 < x < 30
total integer values = 29 - 11 + 1 = 19

Answer B.
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 10:24
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If the lengths of the sides of a triangle are 10, 20 and x, where x is a positive integer, how many values can x take?

A. 18
B. 19
C. 20
D. 21
E. 22

difference of other two sides < side of a triangle < sum of the other two sides

20-10 < x < 10 + 20; 10 < x < 30

total possible values of x: 19
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 11:38
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x<20+10 --> x<30
x>20-10 --> x>10

Smallest and largest integer values between 10 and 30 are 11 and 29.
29-11+1 = 29-10=19

19 values
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 16:03
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10,20,C
a-b<c<a+b
10<C<30
29-11+1=19 (inclusive)

Ans (B)
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 16:18
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The answer is B.

20-10 < x < 20+10
10 < x < 30

Therefore, x = 19 integers

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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 18:25
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We are to determine the possible number of lengths of the third side of a triangle that has two sides of length 10 and 20, given that the third side is an integer.

x<10+20 and 20<x+10
=> 10<x<30
Basically we are to determine the number of integer of x within the given range above
=29-11+1 = 18+1=19.

The answer is B.
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 19:31
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In order 10,20 and x to be lengths of sides of a triangle, the following features must be done:
10+20 > x —> x < 30
20+x >10 —> x > —10
x +10 >20 —> x > 10
———————————
—> 10 < x < 30
x can take (29–11)+1 = 19 values

The answer is B

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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 20:12
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the value of x should be of the form 10<x<30 so b will be the answer.
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   05 Mar 2020, 00:01
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If the lengths of the sides of a triangle are 10, 20 and x, where x is a positive integer, how many values can x take?

A. 18
B. 19
C. 20
D. 21
E. 22
Two properties:
(1) The sum of two sides are greater than the third longest side
(2) The difference between two sides is less than the third longest
If 20 is the longest side and x > 10 then 10 + x > 20 and x- 10 <20
10 + x > 20
Or, x > 10
And x- 10 <20
Or, x<30
The value of x = 10<x<30
X = 19
Answer: 19(B)
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink] New post   04 Mar 2020, 09:16
third side of the ∆ has to be less than the sum of two other sides and greater than the difference of two sides
in this case the value of x can be
10<x<30
total possible values (29-11+1) ; 19
IMO B


If the lengths of the sides of a triangle are 10, 20 and x, where x is a positive integer, how many values can x take?

A. 18
B. 19
C. 20
D. 21
E. 22
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Re: If the lengths of the sides of a triangle are 10, 20 and x, where x is [#permalink]
04 Mar 2020, 09:16
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