In a parallelogram, The lengths of adjacent sides are 15 cm and 17 cm respectively. If the length of one diagonal is 18 cm, find the length of the other diagonal........

In a parallelogram, The lengths of adjacent sides are 15 cm and 17 cm respectively. If the length of one diagonal is 18 cm, find the length of  the other diagonal........

Sol :  

In a parallelogram, the sum of the squares of the diagonals = 2 x ( the sum of the squares of the two adjacent sides).

Or          (D1)^2 + (D2)^2 = 2{(a)^2 + (b)^2}

Or          18^2 + (D2)^2   = 2 { 15^2 + 17^2 }

Or          324 + (D2)^2    = 2 { 225 + 289}

Or             (D2)^2  =  1028 - 324

Or             D2       = sqrt(704)

Or             D2       =  26.53 cm