Rhombus IV

Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.

Correct answer:

u =  31.305 cm
v =  62.61 cm

Step-by-step explanation:

$$\begin{gathered} u:v=1:2 \\ u=v\mathrm{/}2 \\ {a}^2=(u\mathrm{/}2{)}^2+(v\mathrm{/}2{)}^2 \\ {a}^2=(u\mathrm{/}2{)}^2+(u{)}^2 \\ {a}^2=u^2\mathrm{/}4+u^2 \\ {a}^2=u^2\cdot 5\mathrm{/}4 \\ u={\displaystyle \frac{a}{\sqrt{5\mathrm{/}4}}} \\ u=31.305\text{ cm } \end{gathered}$$

$v=2\cdot 31.305={\displaystyle \frac{6261}{100}}\text{ cm}=62.61\text{ cm}$

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