Triangle A has sides of lengths #48 ,36 #, and #54 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

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To find the possible lengths of the other two sides of triangle B, which is similar to triangle A, we use the property of similar triangles where corresponding sides are proportional.

Let's denote the corresponding sides of triangles A and B as follows:

Triangle A: Side lengths are 48, 36, and 54. Triangle B: Side lengths are x, 5, and y (where x and y are the other two sides we want to find).

Using the property of similar triangles, we set up the following proportion:

[ \frac{x}{48} = \frac{5}{36} = \frac{y}{54} ]

We can solve this proportion to find the possible values of x and y.

[ \frac{x}{48} = \frac{5}{36} ] [ x = \frac{5 \times 48}{36} = \frac{240}{36} = \frac{20}{3} ]

[ \frac{y}{54} = \frac{5}{36} ] [ y = \frac{5 \times 54}{36} = \frac{270}{36} = \frac{15}{2} ]

So, the possible lengths of the other two sides of triangle B are ( \frac{20}{3} ) and ( \frac{15}{2} ).