# Rhombus

Calculate the perimeter and area of ​​a rhombus whose diagonals are 39 cm and 51 cm long.

Correct result:

p =  128.406 cm
S =  994.5 cm2

#### Solution:

$u_{1}=39 \ \text{cm} \ \\ u_{2}=51 \ \text{cm} \ \\ \ \\ a^2=(u_{1}/2)^2+(u_{2}/2)^2 \ \\ a=\sqrt{ (u_{1}/2)^2+(u_{2}/2)^2 }=\sqrt{ (39/2)^2+(51/2)^2 } \doteq 32.1014 \ \text{cm} \ \\ \ \\ p=4 \cdot \ a=4 \cdot \ 32.1014=6 \ \sqrt{ 458 }=128.406 \ \text{cm}$

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