Diamond diagonals

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

Result

u =  21.633 cm
v =  14.422 cm

Solution:


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v=2⋅ S/u=2⋅ 156/21.6333≐14.4224=14.422  cm   v=u2  S2=u⋅ v2=21.6333⋅ 14.42242=156 cm2 a2=(u/2)2+(v/2)2=(21.6333/2)2+(14.4224/2)2≐12.9999 cmv = 2 \cdot \ S/u = 2 \cdot \ 156/21.6333 \doteq 14.4224= 14.422 \ \text { cm } \ \\ \ \\ v = u_{ 2 } \ \\ \ \\ S_{ 2 } = \dfrac{ u \cdot \ v }{ 2 } = \dfrac{ 21.6333 \cdot \ 14.4224 }{ 2 } = 156 \ cm^2 \ \\ a_{ 2 } = \sqrt{ (u/2)^2+(v/2)^2 } = \sqrt{ (21.6333/2)^2+(14.4224/2)^2 } \doteq 12.9999 \ cm

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