SOLUTION: Picture of a rectangle that represents a floor that is 20 x 15. Another rectangle inside that one representing an area rug. The rug and the floor are similar rectangles with peri

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Question 416861: Picture of a rectangle that represents a floor that is 20 x 15. Another rectangle inside that one representing an area rug. The rug and the floor are similar rectangles with perimeters in the ratio of 5 to 3. What is the area of the rug?
I'm thinking I'm doing proportions but not sure how to do it.
Thanks
Found 2 solutions by sudhanshu_kmr, ewatrrr:
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Here rug and the floor are similar rectangle.......
perimeters are in ratio 5: 3
so, dimension are 20 * 3 / 5 = 12
and 15 * 3 /5 = 9
so, dimension is 12 x 9
area = 12*9 = 108 unit square.....


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

perimeters in the ratio of 5 to 3

floor that is 20 x 15: P =70

Let x represent the P of the rug

  5%2F3+=+70%2Fx       |Cross Multiplying to solve for x

   5x = 210

    x = 42, the perimeter of the rug. (OR 21 the sum of its length and width)

The rug and the floor are similar rectangles

  20%2F15+=+%2821-x%29%2Fx  |Cross Multiplying to solve for x

   20x = 15*(21-x)

   35x = 15*21

     x = 15*21/35

     x = 9   the rug is 12 x 9.  It's area is 108 

CHECKING our Answer***

 20/15 = 12/9 = 4/3