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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Question 201289: 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 ?
Found 2 solutions by josmiceli, edjones:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let A%5B1%5D = the area of the larger square
Let A%5B2%5D = the area of the smaller square
Let x = the side of the larger square
Let y = the side of the smaller square
given:
A%5B1%5D+%2F+A%5B2%5D+=+6+%2F+1
-------------------------
A%5B1%5D+=+x%5E2 definition
A%5B2%5D+=+y%5E2 definition
Substituting:
x%5E2+%2F+y%5E2+=+6+%2F+1
Take the square roots of both sides
x+%2F+y+=+sqrt%286%29+%2F+1
Also by definition,
larger diagonal = sqrt%282%29%2Ax
Smaller diagonal = sqrt%282%29%2Ay
larger diagonal / smaller diagonal = %28sqrt%282%29%2Ax%29+%2F+%28sqrt%282%29%2Ay%29
larger diagonal / smaller diagonal = x%2Fy
larger diagonal / smaller diagonal = sqrt%286%29%2F1 answer

Answer by edjones(8007) About Me  (Show Source):
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