# Rhombus

The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height

Result

a =  2.702 cm
h =  2.642 cm

#### Solution:

$u=4.2 \ \text{cm} \ \\ v=3.4 \ \text{cm} \ \\ \ \\ a=\sqrt{ (u/2)^2+(v/2)^2 }=\sqrt{ (4.2/2)^2+(3.4/2)^2 } \doteq 2.7019 \doteq 2.702 \ \text{cm}$
$S=u \cdot \ v / 2=4.2 \cdot \ 3.4 / 2=\dfrac{ 357 }{ 50 }=7.14 \ \text{cm}^2 \ \\ \ \\ S=a \cdot \ h \ \\ h=S/a=7.14/2.7019 \doteq \dfrac{ 510 }{ 193 } \doteq 2.6425 \doteq 2.642 \ \text{cm}$

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