Rhombus

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

Correct answer:

p =  128.4056 cm
S =  994.5 cm²

Step-by-step explanation:

$$\begin{gathered} u_1=39\text{ cm } \\ {u}_2=51\text{ cm } \\ {a}^2=(u_1\mathrm{/}2{)}^2+(u_2\mathrm{/}2{)}^2 \\ a=\sqrt{(u_1\mathrm{/}2{)}^2+(u_2\mathrm{/}2{)}^2}=\sqrt{(39\mathrm{/}2{)}^2+(51\mathrm{/}2{)}^2}\doteq 32.1014\text{ cm } \\ p=4\cdot a=4\cdot 32.1014=6\sqrt{458}=128.4056\text{ cm} \end{gathered}$$

$S={\displaystyle \frac{u_1\cdot u_2}{2}}={\displaystyle \frac{39\cdot 51}{2}}={\displaystyle \frac{1989}{2}}{\text{cm}}^2=994.5{\text{cm}}^2$

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