Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm2 and the side is 13 cm long.

Correct answer:

u =  21.6333 cm
v =  14.4222 cm

Step-by-step explanation:

S=156 cm2 a=13 cm  S = ah = 2uv  h=S/a=156/13=12 cm  (u/2)2+(v/2)2 = a2  u2+v2 = 4a2 u2+v2 = 1352  uv= 2S = 312  u2 + (2S/u)2 = 4a2 u2 + 3122/u2 = 676  x = u2  x + 97344/x = 676 x2+97344=676x  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  u1=x1=468=6 1321.6333 u2=x2=208=4 1314.4222  u=u1=21.6333=6 13=21.6333 cm

Our quadratic equation calculator calculates it.

v=2 S/u=2 156/21.6333=4 1314.4222 cm  v= u2  S2=2u v=221.6333 14.4222=156 cm2 a2=(u/2)2+(v/2)2=(21.6333/2)2+(14.4222/2)2=13 cm

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: