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 =  42 cm
h =  33.6 cm

Step-by-step explanation:

$$\begin{gathered} a=35\text{cm} \\ u=56\text{cm} \\ {a}^2=(u/2{)}^2+(v/2{)}^2 \\ v=2\cdot \sqrt{a^2-(u/2{)}^2}=2\cdot \sqrt{35^2-(56/2{)}^2}=42\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=S_2 \\ a\cdot h=\frac{1}{2}u\cdot v \\ ah=u\cdot v/2 \\ h=\frac{u\cdot v}{2\cdot a}=\frac{56\cdot 42}{2\cdot 35}=33.6\text{cm} \end{gathered}$$

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