SOLUTION: The ratio of the areas of two squares is 6:1. find the corresponding ratio of the lengths of the diagonals of the two squares ?

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let = the area of the larger square
Let = the area of the smaller square
Let = the side of the larger square
Let = the side of the smaller square
given:

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definition
definition
Substituting:

Take the square roots of both sides

Also by definition,
larger diagonal =
Smaller diagonal =
larger diagonal / smaller diagonal =
larger diagonal / smaller diagonal =
larger diagonal / smaller diagonal = answer

You can put this solution on YOUR website!
Let s=length of a side and A=area
s^2=A
when s=1 then area=1
when s=sqrt(6) the area=6
The length of the diagonals can be found using a^2+b^2=c^2
1+1=2
diagonal =sqrt(2)
6+6=12
diagonal = sqrt(12)
=sqrt(4*3)
=2sqrt(3)
The ratio of the lengths of the diagonals is 2sqrt(3):sqrt(2)
.
Ed