Question 557093: in a parallelogram one side is 13 meter and another is 11 meters and one of the diagonals is 16 meters.
find the other diagonal
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! http://www.math10.com/en/geometry/parallelogram.html>
the answer to your question lies in the reference.
if you allow a and b to be equal to the sides of your parallelogram, and if you allow p and q to be equal to the diagonals of your parallelogram, then the relationship between the sides and the diagonals is given by the formula:
p^2 + q^2 = 2 * (a^2 + b^2)
in your parallelogam, you can assign values as follows:
a = 13
b = 11
p = 16
q = x
the formula becomes:
16^2 + x^2 = 2 * (13^2 + 11^2)
simplify to get:
256 + x^2 = 2 * (169 + 121)
simplify further to get:
256 + x^2 = 580
subtract 256 from both sides of this equation to get:
x^2 = 580 - 256 which becomes:
x^2 = 324
take the square root of both sides of this equation to get:
x = 18
that's your answer.
the length of the other diagonal is equal to 18 meters
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if you did not know the formula, then you could have found it the hard way by using the pythagorean formula on right triangles formed from the parallelogram. i did it that way to convince myself that i could get the same answer. i did get the same answer, so i'm comfortable with the formula. using the formula is much easier.
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