Question

In the given square, a diagonal is drawn and parallel line segments joining points on the adjacent sides are drawn on both sides of the diagonal. The length of the diagonal is $n \sqrt { 2 }$cm. If the distance between consecutive line segments be then the sum of the lengths of all possible line segments and the diagonal is

• A.
• B.
• C. $n ( n + 2 ) c m$
• D. $n ^ { 2 } \sqrt { 2 } \mathrm {~cm}$

Answer 1

Answer: (D)

$n ^ { 2 } \sqrt { 2 } \mathrm {~cm}$

Answer 2

Let us consider the diagonal and an adjacent parallel line

Length of the line PQ = RS = AC – (AR + SC) = AC – 2AR

= AC ­­– 2.PR ($\bullet \bullet$ AR = PR)

= $n \sqrt { 2 } - 2 \cdot \frac { 1 } { \sqrt { 2 } } = n \sqrt { 2 } - \sqrt { 2 } = ( n - 1 ) \sqrt { 2 } \mathrm {~cm}$

Length of line adjacent to PQ, other than AC, will be

∴ Sum of the lengths of all possible line segments and the

diagonal

,