Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.

Correct result:

u =  21.6333 cm
v =  14.4222 cm

Solution:

S=156 cm2 a=13 cm  S=ah=uv2  h=S/a=156/13=12 cm  (u/2)2+(v/2)2=a2  u2+v2=4a2 u2+v2=1352  uv=2S=312  u2+(2S/u)2=4a2 u2+3122/u2=676  x=u2  x+97344/x=676 x2+97344=676x  x2676x+97344=0  a=1;b=676;c=97344 D=b24ac=67624197344=67600 D>0  x1,2=b±D2a=676±676002 x1,2=676±2602 x1,2=338±130 x1=468 x2=208   Factored form of the equation:  (x468)(x208)=0  u1=x1=468=6 1321.6333 u2=x2=208=4 1314.4222  u=u1=21.6333=6 13=21.6333 cm

Our quadratic equation calculator calculates it.

v=2 S/u=2 156/21.6333=4 1314.4222=14.4222 cm  v=u2  S2=u v2=21.6333 14.42222=156 cm2 a2=(u/2)2+(v/2)2=(21.6333/2)2+(14.4222/2)2=13 cm



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