SOLUTION: If two Rectangles are similar and Rectangle A has and area of 180ft^2 and a lenght of 20ft, and rectangle B has an area of 45 ft ^2. What is the perimeter of rectangle B?

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Question 934339: If two Rectangles are similar and Rectangle A has and area of 180ft^2 and a lenght of 20ft, and rectangle B has an area of 45 ft ^2. What is the perimeter of rectangle B?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangle A:
L and w for length and width.
wL=180
w%2A20=180
w=9, the width of rectangle A.

The lengths for width and length of rectangle B are some factor k of w and L. k%3C1 since we know rectangle B is smaller area while being similar to rectangle A.

Rectangle B:
%28kw%29%28kL%29=45, and we already now know w and L.
k%5E2%2AwL=45, and we also were given wL=180.
k%5E2=45%2F%28wL%29
k%5E2=45%2F180
k%5E2=%281%2F4%29
highlight%28k=1%2F2%29

The perimeter for rectangle B using the factor k,
2%2A%281%2F2%29w%2B2%2A%281%2F2%29L
w%2BL
9%2B20
highlight%28perimeterOfRectangleB=29%29