SOLUTION: if the peremeter of a rectangle and a square are equal and the ratio of 2 adjecent sides of the rectangle ais 1:2, then find the ratio of their areas

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Question 847449: if the peremeter of a rectangle and a square are equal and the ratio of 2 adjecent sides of the rectangle ais 1:2, then find the ratio of their areas
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The square, side s.
Perimeter is 4s and area is s%5E2.

The rectangle, sides x and 2x.
Perimeter is 2%2Ax%2B2%2A2x=6x.

Both perimeters are specified to be equal.
4s=6x
2s=3x.
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Solving for s, s=%283%2F2%29x and this is to be used for finding area for the square and for the rectangle, as expressions.

Area for the square: %28%283%2F2%29x%29%5E2=highlight%28%289%2F4%29x%5E2%29.
Area for the rectangle: x%2A2x=highlight%282x%5E2%29.
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RATIO of the areas of the square to the rectangle:
%28%289%2F4%29x%5E2%29%2F%282x%5E2%29
%289%2F4%29%2F2
highlight%289%2F8%29.