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Algebra

The sides of a triangle are distinct positive integers in arithmetic progression. If the smallest side is 10 the number of such triangles is ….........

Profile image of aylmer Britto R
11 Years agoGrade
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4 Answers

Profile image of Ashwin
11 Years ago
hi,
 
Since the sides are in A.P let the sides be x , x + d and x + 2d.
now since smallest side is 10 
 
therefore x = 10 
=> sides are 10 , 10 + d and 10 + 2d 
 
we know that sum of any two sides of a triangle is greater than the third side 
=> 20 + d > 10 +2d
=> 10 + d > 2d
since we know that the sign of d = + therefore we can subtract d
10 > d
=> d
since the sides are positive integers
therefore ,
d can hold the values 1 , 2 ,3 ….., 9
 
therefores number of triangles which are possible is 9 . 
 
Regards, 
Ashwin
 
Profile image of Ashwin
11 Years ago
in the last third line it is 
=> d
instead it should be 
=> d
 
sorry my mistake
Profile image of Ashwin
11 Years ago
d
Profile image of Ashwin
11 Years ago
its not coming take it as 10 > d so d should be less than 10 

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