SOLUTION: Two square have their sides in the ration 2:3. What is the ration of their 1) Perimeter 2) Area

Algebra ->  Parallelograms -> SOLUTION: Two square have their sides in the ration 2:3. What is the ration of their 1) Perimeter 2) Area      Log On


   

Question 917723: Two square have their sides in the ration 2:3. What is the ration of their
1) Perimeter
2) Area
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
s= side length for the smaller square
S= side length for the larger square
s%2FS=2%2F3

1) 4s= perimeter for the smaller square
4S= perimeter for the larger square
The ratio of the perimeters is
4s%2F4S=%284%2F4%29%28s%2FS%29=1%2A%282%2F3%29=2%2F3

2) s%5E2= area for the smaller square
S%5E2= area for the larger square
The ratio of the areas is
s%5E2%2FS%5E2=%28s%2FS%29%5E2=%282%2F3%29%5E2=2%5E2%2F3%5E2=4%2F9

NOTE: For similar shapes (two squares, two cubes, two circles, two spheres, etc),
all measures of length (side, perimeter, radius, diameter, circumference, etc) are in the same ratio.
If that ratio is r ,
The ratio of corresponding areas is r%5E2 ,
and the ratio of corresponding volumes is r%5E3 .
That works for any kind of shape, as long as one is a scaled up or scaled down version of the other.