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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
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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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
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
