Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm² and side is 13 cm long.

Correct result:

u =  21.6333 cm
v =  14.4222 cm

Solution:

Our quadratic equation calculator calculates it.

$$\begin{gathered} v=2\cdot S\mathrm{/}u=2\cdot 156\mathrm{/}21.6333=4\sqrt{13}\doteq 14.4222=14.4222\text{ cm } \\ v=u_2 \\ {S}_2={\displaystyle \frac{u\cdot v}{2}}={\displaystyle \frac{21.6333\cdot 14.4222}{2}}=156{\text{cm}}^2 \\ {a}_2=\sqrt{(u\mathrm{/}2{)}^2+(v\mathrm{/}2{)}^2}=\sqrt{(21.6333\mathrm{/}2{)}^2+(14.4222\mathrm{/}2{)}^2}=13\text{ cm} \end{gathered}$$

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