Diagonals of a rhombus 2

One diagonal of a rhombus is greater than the other by 4 cm. If the area of the rhombus is 96 cm2, find the side of the rhombus.

Correct answer:

a =  10 cm

Step-by-step explanation:

u = 4 cm + v S=96 cm2  S = 2uv​ = 2(4+v)v​  96=(4+v)⋅ v/2  96=(4+v)⋅ v/2 −0.5v2−2v+96=0 0.5v2+2v−96=0  a=0.5;b=2;c=−96 D=b2−4ac=22−4⋅0.5⋅(−96)=196 D>0  v1,2​=2a−b±D​​=1−2±196​​=−2±141​ v1,2​=−2±14 v1​=12 v2​=−16  v=v1​=12 cm u=4+v=4+12=16 cm  a=(u/2)2+(v/2)2​=(16/2)2+(12/2)2​=10 cm

Our quadratic equation calculator calculates it.


Try another example


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 are looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

algebraarithmeticplanimetricsUnits of physical quantitiesGrade of the word problem

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

Related math problems and questions: