Two diagonals

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

Correct result:

o =  17.8885 cm

Solution:

u1=8 cm u2:u1=1:2 u2=1/2⋅ u1=1/2⋅ 8=4 cm  a2=(u1/2)2+(u2/2)2  a=(u1/2)2+(u2/2)2=(8/2)2+(4/2)2=2 5 cm≐4.4721 cm  o=4⋅ a=4⋅ 4.4721=8 5≐17.8885=17.8885 cm   Verifying Solution:  t=u2/u1=4/8=12=0.5

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