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Kailash is drawing a square pattern. he draws 1 square in the first row . he draws 2 squares in second row and 3 in third row . how many rows can be make

if he draws 45 squares in total. please answer with procedure

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Using formula of sum of n th term s(total sum) = n/2(2a + (n - 1)d ) where s = sum or here total squares = 45 a = 1st term or here no of square in 1st row = 1 n = no of terms or here no. of rows = n(let) d = common difference or here no of squares which increase in each row = 1 so 45 = n/2(2 + n - 1 ) ⇒90= n(n + 1) ⇒n² + n - 90 = 0 doing middle term ⇒ n² +10n - 9n - 90 = 0 ⇒n(n + 10) - 9(n + 10) = 0 ⇒(n- 9)(n + 10 ) = 0 so n - 9 = 0⇒n = 9 and n + 10 = 0 ⇒ n = - 10 which is not possible so 9 rows is the answer.