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 0.5v22v+96=0 0.5v2+2v96=0  a=0.5;b=2;c=96 D=b24ac=2240.5(96)=196 D>0  v1,2=2ab±D=12±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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