# 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:

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

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