# 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:

$a=12 \ \\ u_{1}=21 \ \\ a^2=(u_{1}/2)^2 +(u_{2}/2)^2 \ \\ u_{2}=2 \cdot \ \sqrt{ a^2-(u_{1}/2)^2 }=2 \cdot \ \sqrt{ 12^2-(21/2)^2 } \doteq 3 \ \sqrt{ 15 } \doteq 11.619 \doteq 11.619 \ \text{cm}$

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