If the sides of a square measure 10√6 units, then find the length of the diagonal?

1 Answer
Jim G.
Jun 24, 2018

#"diagonal "=20sqrt3#

Explanation:

#"the diagonal splits the square into 2 right triangles"#

#"the diagonal is therefore the hypotenuse of one triangle"#

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

#"hypotenuse (h)"^2="sum of squares on other 2 sides"#

#h^2=(10sqrt6)^2+(10sqrt6)^2#

#h=sqrt(600+600)=sqrt1200#

#color(white)(xxxxxxxxxxx)=sqrt(400xx3)#

#color(white)(xxxxxxxxxxx)=sqrt400xxsqrt3=20sqrt3#

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