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Please help! Some identical balls are arranged in rows to form an equilateral triangle . The first row consists of one ball , the second row consists of of two balls and so on . If 99 more identical balls are added to the total number of balls used i

Some identical balls are arranged in rows to form an equilateral triangle . The first row consists of one ball , the second row consists of  of two balls and so on . If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle , then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains . Then the number of balls used to form the equilateral triangle is :

  • Option 1)

    157

  • Option 2)

    262

  • Option 3)

    225

  • Option 4)

    190

 
Answers (1)
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let total number of rows in forming equilateral triangle is n 

then 

\\\frac{n(n+1)}{2}+99=(n-2)^{2}\\\\\:n=19

no. \:\:of\:\: balls =\frac{19\times20}{2}=190

option 4 is answer

 


Option 1)

157

Option 2)

262

Option 3)

225

Option 4)

190

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