Diamond diagonals

Calculate the diamond's diagonal lengths if its area is 156 cm2 and the side length is 13 cm.

Correct answer:

u =  21.6333 cm
v =  14.4222 cm

Step-by-step explanation:

S=156 cm2 a=13 cm S = uv/2 a2 = (u/2)2+(v/2)2 4a2 = u2 + v2 676 = u2+v2 312 = uv v = 312/u 676 = u2+(312/u)2 x = u2 676 = x+3122/x  676x=x2+3122  x2+676x97344=0 x2676x+97344=0  a=1;b=676;c=97344 D=b24ac=67624197344=67600 D>0  x1,2=2ab±D=2676±67600 x1,2=2676±260 x1,2=338±130 x1=468 x2=208  u=x1=468=6 13=21.6333 cm

Our quadratic equation calculator calculates it.

v=x2=208=4 13=14.4222 cm

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