# 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) $190$

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 1)

$157$

Option 2)

$262$

Option 3)

$225$

Option 4)

$190$

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