Diagonals of a rhombus 2

One diagonal of a rhombus is greater than the other by 4 cm. If the area of the rhombus is 96 cm2, find the side of the rhombus.

Correct answer:

a =  10 cm

Step-by-step explanation:

u = 4 cm + v S=96 cm2  S = 2uv​ = 2(4+v)v​  96=(4+v)⋅ v/2  96=(4+v)⋅ v/2 −0.5v2−2v+96=0 0.5v2+2v−96=0  a=0.5;b=2;c=−96 D=b2−4ac=22−4⋅0.5⋅(−96)=196 D>0  v1,2​=2a−b±D​​=1−2±196​​=−2±141​ v1,2​=−2±14 v1​=12 v2​=−16  v=v1​=12 cm u=4+v=4+12=16 cm  a=(u/2)2+(v/2)2​=(16/2)2+(12/2)2​=10 cm

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