Question

A square and a rhombus are of same side 'a' cm.if the area of a square is twice the area of rhombus then sum of the diagonal of rhombus is
(1) 3√2a cm
(2) √6a cm
(3) 3√3a cm
(4) 2√3a cm

Answer 1

Answer:

Step-by-step explanation:

Area of Rhombus = 1/2 * (Area of  Square)

                             = 1/2 * ( a²)

and Area of Rhombus = 1/2 * d1 * d2

          1/2 * ( a²) = 1/2 * d1 * d2

          d1 * d2 = a²

          diagonal of Rhombus bisects each other at 90°

         By pythagorus theorem

        a² = (d1/2)² +  (d2/2)²

        a² = (d1)²/4 +  (d2)²/4

       4a² = (d1)² + (d2)²

       (d1+d2)² = (d1)² + (d2)² + 2*d1*d2

                     =  4a² + 2a²

                    = 6a²

       d1+d2 = √6a²

                 = √6 a cm