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:

$a=4 \ \\ u_{1}=6.4 \ \\ a^2=(u_{1}/2)^2 +(u_{2}/2)^2 \ \\ u_{2}=2 \cdot \ \sqrt{ a^2-(u_{1}/2)^2 }=2 \cdot \ \sqrt{ 4^2-(6.4/2)^2 }=\dfrac{ 24 }{ 5 }=4.8 \ \text{cm}$

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