Match each description with the expression containing terms that model it
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Similar polygons only differ by a scaling factor. In other words, two polygons are similar if one is the scaled version of the other.
In particular, this implies that the angles are preserved, and the correspondent sides are in proportion.
These two polygons are both rectangles, so the angles are preserved. We must check the sides, and we have to check if the smaller sides are in the same proportion as the bigger sides.
So, the two rectangles are similar if the following is true.
In any proportion, the product of the inner terms must be the same as the product of the outer terms:
This is clearly false, and thus the two rectangles are not similar.
The area of a rectangle is the product of its dimensions
The dimensions of the rectangle are: and
The area is given as:
Express 125 as 5^3
Apply difference of cubes
The area of a rectangle is:
So, by comparison:
Read more about areas at: