Diagonals in diamons/rhombus

Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.

Result

u2 =  4.8 cm

Solution:

a=4 u1=6.4 a2=(u1/2)2+(u2/2)2 u2=2⋅ a2−(u1/2)2=2⋅ 42−(6.4/2)2=245=4.8 cma=4 \ \\ u_{1}=6.4 \ \\ a^2=(u_{1}/2)^2 +(u_{2}/2)^2 \ \\ u_{2}=2 \cdot \ \sqrt{ a^2-(u_{1}/2)^2 }=2 \cdot \ \sqrt{ 4^2-(6.4/2)^2 }=\dfrac{ 24 }{ 5 }=4.8 \ \text{cm}

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