# Triangle A has sides of lengths #51 #, #45 #, and #33 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

Since triangles A & B are similar, their sides will be in the same proportion.

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

Let's denote the sides of triangle A as ( a = 51 ), ( b = 45 ), and ( c = 33 ), and the corresponding sides of triangle B as ( x ) and ( y ).

Since triangle B is similar to triangle A, the ratio of the lengths of corresponding sides in both triangles will be equal:

[ \frac{x}{51} = \frac{y}{45} = \frac{7}{33} ]

From this proportion, we can solve for ( x ) and ( y ) by setting up two equations:

[ \begin{cases} \frac{x}{51} = \frac{7}{33} \ \frac{y}{45} = \frac{7}{33} \end{cases} ]

Solving these equations will give us the possible lengths of ( x ) and ( y ). We can do this by cross-multiplying and then solving for ( x ) and ( y ):

For ( x ): [ x = \frac{7}{33} \times 51 ]

For ( y ): [ y = \frac{7}{33} \times 45 ]

Calculating these values will give us the possible lengths of the other two sides of triangle B:

[ x = \frac{7}{33} \times 51 = \frac{119}{11} ]

[ y = \frac{7}{33} \times 45 = \frac{105}{11} ]

Therefore, the possible lengths of the other two sides of triangle B are ( \frac{119}{11} ) and ( \frac{105}{11} ).

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