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# What is the length of the sides of a rhombus whose diagonals are 40 and 96?

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What is the length of the sides of a rhombus whose diagonals are 40 and 96?

Jul 8, 2014

#2
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In a rhombus each diagonal bisects the other to form 4 right triangles.  The side lengths of these triangles will be half the diagonal lengths since the diagonals were bisected.  This leaves us triangles with side lengths of 20 and 48 with the hypotenuse being a side length of the rhombus.  Apply the pythagorean theorem:

20^2+48+2=h^2

400+2304=h^2

2704=h^2

sqrt(2704)=h

52=h

Jul 8, 2014

#1
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The diagonals are the sides of a rhombus?

Jul 8, 2014
#2
+576
+13

In a rhombus each diagonal bisects the other to form 4 right triangles.  The side lengths of these triangles will be half the diagonal lengths since the diagonals were bisected.  This leaves us triangles with side lengths of 20 and 48 with the hypotenuse being a side length of the rhombus.  Apply the pythagorean theorem:

20^2+48+2=h^2

400+2304=h^2

2704=h^2

sqrt(2704)=h

52=h

jboy314 Jul 8, 2014
#3
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jboy314, that is a great answer.

Jul 8, 2014
#4
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Thank you jboy314 :)

Jul 8, 2014
#5
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woohoo! happy to help

Jul 8, 2014