The sides of a right angled triangle are all integers.Two sides are primes that differ by 50.The smallest possible value of the third side is ............

  • 60
  • 57
  • 53
  • 49

Let the two sides be a and b ,where a is prime,
Since,the third side differ by a by 50
so the third side = 50 + a.

Now, by pythagoras theorem,
    a2 + b2  = (a+50)2a2 + b2  = a2 + 100a +2500b2 = 100 a + 2500
  Now,the minimum value of a to satisfy the equation and b to be an integer,is 11
 
i,e,   b2=100×11 + 2500b = 3600 = 60 
Thus,the sides of the triangle are 11,60,61

Thus,the smallest possible value of third side is 60.

  • -1

I THINK THE ANSWER IS 53

  • -1
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