Diamond diagonals

Calculate the diamond's diagonal lengths if its area is 156 cm2 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

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 system of equations and are looking for calculator system of linear equations?
Do you want to convert length units?
The Pythagorean theorem is the base for the right triangle calculator.

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

Units of physical quantities:

Grade of the word problem:


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

Related math problems and questions: