Diagonals of the rhombus

How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm2?

Correct answer:

e =  4.4721 cm
f =  8.9443 cm

Step-by-step explanation:

a=5 cm S=20 cm2  S = a h h=S/a=20/5=4 cm  h = a   sin(A) A=π180°arcsin(h/a)=π180°arcsin(4/5)53.1301   e=a 22 cosA=a 22 cos53.130102354156° =5 22 cos53.130102354156° =5 22 0.6=4.472=4.4721 cm
f=a 2+2 cosA=a 2+2 cos53.130102354156° =5 2+2 cos53.130102354156° =5 2+2 0.6=8.94427=8.9443 cm   Verifying Solution:  S = EF/2 (E/2)2 + (F/2)2 = a2  (E/2)2 + (2 S/E/2)2 = a2 E2 + 4 S2/E2 = 4 a2 z = E2  z + 4 S2/z = 4 a2  z2+4 S2=4 a2 z  z2+4 202=4 52 z z2100z+1600=0  a=1;b=100;c=1600 D=b24ac=1002411600=3600 D>0  z1,2=2ab±D=2100±3600 z1,2=2100±60 z1,2=50±30 z1=80 z2=20  z=z1=80  E=z=80=4 5 cm8.9443 cm F=2 S/E=2 20/8.9443=2 5 cm4.4721 cm

Our quadratic equation calculator calculates it.




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.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3   video4

Related math problems and questions: