SOLUTION: The ratio of the areas of 2 squares is 6:7. If the perimeter of the larger square is 73.5 what is the perimeter of the smaller aquare? Please help me solve them. Thank youuuu so mu

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the areas of 2 squares is 6:7. If the perimeter of the larger square is 73.5 what is the perimeter of the smaller aquare? Please help me solve them. Thank youuuu so mu      Log On


   

Question 914497: The ratio of the areas of 2 squares is 6:7. If the perimeter of the larger square is 73.5 what is the perimeter of the smaller aquare? Please help me solve them. Thank youuuu so much 😊😊😊
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the side lengths of the smaller and larger squares are s and S respectively,
the perimeters are 4%2As and 4%2AS respectively,
with 4%2AS=73.5
The ratio of their sides and perimeters is s%2FS=4%2As%2F4S ,
and the ratio of their areas is s%5E2%2FS%5E2 .
We know that s%5E2%2FS%5E2=6%2F7 .
s%5E2%2FS%5E2=6%2F7-->%28s%2FS%29%5E2=6%2F7-->4%2As%2F4S=sqrt%286%2F7%29-->4%2As=sqrt%286%2F7%29%2A%284%2AS%29
So, 4%2As=sqrt%286%2F7%29%2A73.5--->4%2As=highlight%2868.0%29 (rounded).

NOTES:
In general, when you have similar shapes (same figure, or 3-D solid, but scaled up or down),
if the ratio of length measures (side lengths, perimeters, circumferences, etc) is R,
then the ratio of the corresponding areas is R%5E2 ,
and (if the similar shapes are 3-dimensional) the ratio of the volumes is R%5E3 .
The larger square is a scaled up version of the smaller square, so that applies.
(We could not say the same of triangles, or rectangles).