What is the perimeter of a rhombus whose diagonals are 16 and 30?

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Answer 1 · 2016-12-25T01:51:14

#68#

enter image source here

Some of the rhombus' properties:

a) The sides of a rhombus are all congruent. (the same length).
#=> AB=BC=CD=DA#

b) The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.
#=> AO=OC=1/2AC, and BO=OD=1/2BD#

Now back to our question :

enter image source here

Given that the two diagonals are #30, and 16#,
#=> AO=30/2=15, BO=16/2=8, angleAOB=90^@#

From Pythagorean theorem, we know
#AB^2=AO^2+BO^2#
#=> AB=sqrt(15^2+8^2)=sqrt289=17#

SInce #AB=BC=CD=DA#,
perimeter of #ABCD= 17*4=68#