Diamond

The side length of the 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:

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

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

Try another example