The diamond

The diamond has an area S = 120 cm2, and 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 = 2e f S = 25x 12x  x=5 122 S=5 122 120=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=131209.2308 cm   Verifying Solution:   S1=2e f=210 24=120

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