Diamond diagonals

Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square 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+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​=2a−b±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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