a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
"suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 96 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 96 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 96 ( 2 r - 4 ) * r = 96 2 r ^ 2 - 4 r - 96 = 0 r can not be negative so r = 8 and c = 12 so , answer will be c"
divide(96, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(96, 2))))), 2))