Question 1187561
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If the rug is half the length of the room and also half the width, then the rug and the room are similar figures (scale models of each other) with a scale ratio 1:2.<br>
In any similar figures, if the ratio of linear measurements (e.g., length and width) is a:b, then the ratio of area measurements is a^2:b^2.<br>
In your problem, since the scale factor is 1:2, the ratio of area measurements is 1:4.<br>
ANSWER: The ratio of the rug's area to the area of the room is 1:4<br>
It will help to understand this concept if you put some example numbers to the problem.<br>
room 10*16; area 160; rug 5*8; area 40; 40 is 1/4 of 160<br>
room 12*20; area 240; rug 6*10; area 60; 60 is 1/4 of 240<br>
etc., etc....<br>