Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm2 and 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=uv2  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=b±D2a=676±676002 x1,2=676±2602 x1,2=338±130 x1=468 x2=208   Factored form of the equation:  (x468)(x208)=0  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.




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






avatar




Tips to related online calculators
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?
Pythagorean theorem is the base for the 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:

  • Diamond diagonals
    kosostvorec Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
  • Diamond diagonals
    kosostvorec Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  • The diamond
    koso The diamond has an area S = 120 cm2, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.
  • Diagonals of a rhombus 2
    rhombus3 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  • Two diagonals
    koso The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
  • Diagonals of the rhombus
    kosostvorec How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  • Rhombus and diagonals
    kosostvorec The rhombus area is 150 cm2, and the ratio of the diagonals is 3:4. Calculate the length of its height.
  • The diamond
    kosodlznik The diamond has sides of 35 cm and the diagonals are in a ratio of 1: 2. Calculate the lengths of the diagonals.
  • Diagonals in the diamond
    kosoctverec_color The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
  • Rhombus and diagonals
    rhombus-diagonals The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides.
  • Diagonals of diamond
    kosostvorec Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
  • Diamond and diagonals
    kosostvorec A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
  • Diamond
    rhombus2 Determine the side of diamond if its content is S = 353 cm2 and one diagonal u2 = 45 cm.
  • Diagonals of a rhombus
    rhombus-diagonals One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
  • Rhombus
    rhombus-diagonals One angle of a rhombus is 136°, and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
  • Diamond side
    diamond-in-square-etc The diagonals of the diamond are 18 cm and 14 cm long. Calculate the length of the diamond side.
  • Diagonals
    koso_uhlopricky Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.