Problem: The difference in the areas of two similar triangles is 18 square feet, and the ratio of the larger area to the smaller is the square of an integer. The area of the smaller triangle, in square feet, is an integer, and one of its sides is feet. The corresponding side of the larger triangle, in feet, is:
Answer Choices:
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Solution:
Let represent the larger, smaller areas, respectively. Since the triangles are similar and is a side of the smaller triangle, we have
a positive integer ; since is an integer, must be divisible by . Only is acceptable. and .
or
Since must equal and must equal . But is the ratio of corresponding sides. It follows that the side of the larger triangle corresponding to side of the smaller triangle is .