Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.

Correct answer:

v =  16.8 cm
u =  42 cm

Step-by-step explanation:

$$\begin{gathered} S_1=S_2 \\ {\displaystyle \frac{1}{2}}av={\displaystyle \frac{1}{2}}{u}_1{u}_2 \\ {\displaystyle \frac{1}{2}}35v={\displaystyle \frac{1}{2}}56u \\ 35v=56u \\ {a}^2=(u_1\mathrm{/}2{)}^2+(u_2\mathrm{/}2{)}^2 \\ 35^2=(56\mathrm{/}2{)}^2+(u\mathrm{/}2{)}^2 \\ v={\displaystyle \frac{1}{4}}\cdot 56\cdot u\mathrm{/}(35)=16.8\text{ cm } \end{gathered}$$

$u=\sqrt{4\cdot 35^2-56^2}=42\text{ cm}$

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