Diamond diagonals

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

Correct result:

u =  21.6333 cm
v =  14.4222 cm

Solution:

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+676x−97344=0 x2−676x+97344=0  a=1;b=−676;c=97344 D=b2−4ac=6762−4⋅1⋅97344=67600 D>0  x1,2=−b±D2a=676±676002 x1,2=676±2602 x1,2=338±130 x1=468 x2=208   Factored form of the equation:  (x−468)(x−208)=0  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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