Two diagonals

The diagonals of the diamond EFGH have lengths in the ratio of 1:2. What is the circumference of a rhombus if the longer diagonal is 8 cm long?

Final Answer:

o =  17.8885 cm

Step-by-step explanation:

$$\begin{gathered} u_1=8\text{cm} \\ {u}_2:u_1=1:2 \\ {u}_2=1/2\cdot u_1=1/2\cdot 8=4\text{cm} \\ {a}^2=(u_1/2{)}^2+(u_2/2{)}^2 \\ a=\sqrt{(u_1/2{)}^2+(u_2/2{)}^2}=\sqrt{(8/2{)}^2+(4/2{)}^2}=2\sqrt{5}\text{cm}\doteq 4.4721\text{cm} \\ o=4\cdot a=4\cdot 4.4721=8\sqrt{5}\doteq 17.8885\text{cm} \\ \text{ Verifying Solution: } \\ t=u_2/u_1=4/8=\frac{1}{2}=0.5 \end{gathered}$$

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