Two diagonals

The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?

Result

u2 =  11.619 cm

Solution:

a=12 u1=21 a2=(u1/2)2+(u2/2)2 u2=2⋅ a2−(u1/2)2=2⋅ 122−(21/2)2≐3 15≐11.619≐11.619 cma=12 \ \\ u_{1}=21 \ \\ a^2=(u_{1}/2)^2 +(u_{2}/2)^2 \ \\ u_{2}=2 \cdot \ \sqrt{ a^2-(u_{1}/2)^2 }=2 \cdot \ \sqrt{ 12^2-(21/2)^2 } \doteq 3 \ \sqrt{ 15 } \doteq 11.619 \doteq 11.619 \ \text{cm}

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