A rhombus with 20 cm sides has a 12 cm diagonal. How long is the other diagonal?

The answer is #4sqrt11 cm#.

1 Answer
Jim G.
Apr 29, 2018

#4sqrt91#

Explanation:

#"using the "color(blue)"rhombus property"#

#• " diagonals are perpendicular bisectors of each other"#

#"then the rhombus is divided into 4 right triangles"#

#"consider the right triangle with legs 6 and x and "#
#"hypotenuse 20"#

#"using "color(blue)"Pythagoras' theorem"#

#20^2=6^2+x^2#

#rArrx=sqrt(20^2-6^2)=sqrt364=2sqrt91#

#rArr"diagonal "=2x=2xx2sqrt91=4sqrt91#

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