The diamond

The diamond has an area S = 120 cm2, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.

Correct answer:

a =  13 cm
h =  9.2308 cm

Step-by-step explanation:

S=120 cm2 e:f=5:12  e=5x f=12x  S=e f2 S=5x 12x2  x=2 S5 12=2 1205 12=2 cm  e=5 x=5 2=10 cm f=12 x=12 2=24 cm  a=(e/2)2+(f/2)2=(10/2)2+(24/2)2=13 cm
S=a h  h=S/a=120/13=120139.2308 cm   Verifying Solution:   S1=e f2=10 242=120



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