Triangle A has sides of lengths #2 ,3 #, and #8 #. Triangle B is similar to triangle A and has a side of length #1 #. What are the possible lengths of the other two sides of triangle B?

True. Sum of the two sides of a triangle is always greater than the third. This is the basic principle of a triangle.

The lengths of the sides of similar triangles are proportional. Therefore, if triangle B is similar to triangle A, the ratio of corresponding sides in triangle B to triangle A will be the same.

Let's denote the length of the corresponding side in triangle B as x. According to the given information, the corresponding side in triangle A is 1.

So, we have the proportion:

1/2 = x/3

Solving for x:

x = 3/2

Now, we can find the lengths of the other two sides of triangle B using the ratios of corresponding sides:

For the side with length 3 in triangle A, the corresponding side in triangle B would be:

3/8 * (3/2) = 9/16

For the side with length 8 in triangle A, the corresponding side in triangle B would be:

8/8 * (3/2) = 3/2

Therefore, the possible lengths of the other two sides of triangle B are 9/16 and 3/2.

Since triangle B is similar to triangle A, their corresponding sides are proportional. Let's denote the lengths of the sides of triangle B as ( x ) and ( y ). According to the similarity of the triangles, we have the following proportion:

[ \frac{x}{2} = \frac{1}{3} \quad \text{(corresponding to the sides 1 and 2)} ]

From this proportion, we can solve for ( x ):

[ x = \frac{2}{3} ]

Similarly, for the sides 1 and 3, we have:

[ \frac{y}{8} = \frac{1}{3} ]

Solving for ( y ):

[ y = \frac{8}{3} ]

Therefore, the possible lengths of the other two sides of triangle B are ( \frac{2}{3} ) and ( \frac{8}{3} ).