One similar figure has an area that is nine times the area of another. The larger figure must have dimensions that are times the

Response:

The area of a shape quantifies the size of a two-dimensional figure, which is typically expressed in square units based on its dimensions. For instance, if we denote a figure's dimensions by k, then its area can be expressed as. In this case, one

similar figure's area is nine times greater than another's. Because the figures share similarity, their areas will exhibit proportional relationships corresponding to their dimensions. Denoting the smaller figure's dimensions as k and the larger's as p times k, we can define the area for the smaller as  and the area for the larger as. Since the area of the larger figure is nine times that of the smaller, it follows that: Consequently, the

larger figure's dimensions must be three times those of the

smaller figure.

T<span>he area of a figure signifies the measure of space within a two-dimensional shape, typically expressed as square units based on the figure's dimensions.

For instance, with a shape having dimensions of k, its area can be given by .
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<span>Consider that one similar figure possesses an area nine times that of another.

As these figures are similar, their areas correspond to the proportionality of their dimensions.

Let the smaller shape's dimensions be k, while the larger is p times the dimensions of the smaller shape. The smaller shape's area is and the larger shape's area is .

Now, knowing the larger figure's area is nine times the area of the smaller figure, we have:

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Thus, the dimensions of the larger figure must be 3 times those of the smaller figure.