SOLUTION: The diagonals of a rhombus have lenghts of 4 and 12. Find the lenght of a side in simplest form. ?

Question 282410: The diagonals of a rhombus have lenghts of 4 and 12. Find the lenght of a side in simplest form. ?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Using the fact that diagonals of a rhombus bisect each other and that they are also perpendicular, we have a right triangle with sides 12/2=6 and 4/2=2 with the hypotenuse being a side s of the rhombus.
By the Pythagorean Theorem we have then:
s^2 = 6^2 + 2^2
s^2 = 36 + 4
s^2 = 40
s = sqrt(40)
s = sqrt(4*10)
s = sqrt(4)*sqrt(10)
s = 2*sqrt(10)

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