Question

In a given square, a diagonal is drawn and parallel line segments joining points on the adjacent sides are drawn on both sides of the diagonals. The length of the diagonal is n√2 cm. If the distance between consecutive line segments is 1/√2 cm, then the sum of the lengths of all possible line segments and the diagonal is

(A)  n(n + 1)√2 cm 

(B)  n² cm 

(C)  n(n + 2) cm 

(D)  n²√2cm

Answer 1

Correct option (D)  n²√2cm

Distance between vertex and diagonal is n/√2 cm. So the sum of distance of all such lines is