# MATH

rectangle ABCD is similar to rectangle wxyz , with AB corresponding to wx. if AB=24,BC=30 and wx=16 , what is the area of the rectangle wxyz

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1. the ratio of areas of similar figures is proportional to the square of their corresponding sides

area of ABCD = 24(30) = 720
WXYZ/720 = 24^2/16^2

solve for WXYZ

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2. The sides should be proportional if they are similar, thus, since AB corresponds with wx, and Ab is 24 while wx is 16, 24/16=1.5 . So ABCD is 1.5 times bigger than wxyz. the other side is 30, CD, is 1.5x bigger than yz, so find that and get the area by multiplying. or u can do a proportion. 24/30=16/x. x=20, which when x by 1.5 is 30

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3. the ratio of the areas is NOT 1.5 : 1
it is 24^2 : 16^2 = 9 : 4

the area of the larger is 720 (see above)
so the area of the smaller is 4/9(720) = 320

You yourself found XY to be 20
so the area of the other rectangle is 16(20) = 320

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4. Rectangle ABCD is similar to rectangle WYYZ.
Uf tge the area of rectangle ABCD is 90 square inches, what is the area of rectangle WXYZ?

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