SOLUTION: The smaller of two similar rectangles has dimensions of 4 and 6. Find the dimension of the larger rectangle if the ratio of the perimeters is 2 to 3

Algebra ->  Rectangles -> SOLUTION: The smaller of two similar rectangles has dimensions of 4 and 6. Find the dimension of the larger rectangle if the ratio of the perimeters is 2 to 3      Log On


   

Question 1202923: The smaller of two similar rectangles has dimensions of 4 and 6. Find the dimension of the larger rectangle if the ratio of the perimeters is 2 to 3
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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small rectangle
dimensions 4 and 6
perimeter 2%2A4%2B2%2A6

large rectangle
dimensions x and y
perimeter 2x%2B2y

Ratio of Perimeters is 2 to 3.
%282%2A4%2B2%2A6%29%2F%282x%2B2y%29=2%2F3

As given, these rectangles are also SIMILAR.
4%2F6=2%2F3=x%2Fy.

system can be system%28%284%2B6%29%2F%28x%2By%29=2%2F3%2C2%2F3=x%2Fy%29.

system%2810%2F%28x%2By%29=2%2F3%2C2%2F3=x%2Fy%29

system%2830=2x%2B2y%2C3x=2y%29

simple substitution is obvious.
30=2x%2B3x-----from which,..... !
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows an exceedingly tedious method for setting up the problem...!

If the ratio of the perimeters is 2:3, then the ratio of each of the dimensions is 2:3.

smaller dimension of larger rectangle: 4(3/2) = 6
larger dimension of larger rectangle: 6(3/2) = 9

ANSWER: 6 by 9