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Two diagonals of a parallelogram have lengths 6 and 8. What is the largest possible length of the shortest side of the parallelogram?

 Feb 1, 2019
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First, label the appropriate diagram of the parallelogram. If the diagonals are perpendicular to each other, then the sides of ABCD has to be 5.

use the equation for obtuse triangles

\(AB^2>25=3^2+4^2=AE^2+BE^2\)

all four angles around E, would be obtuse, which you can figure out to be impossible, so the side can't be longer than 5

 

smiley

 Feb 2, 2019

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