# Triangle A has sides of lengths #2 ,3 #, and #4 #. 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?

Triangle

Triangle

Triangle

Given : triangle A: sides 2, 3, 4, use ratio and proportion to solve for the possibles sides

solve for z:

that completes triangle 1:

God bless...I hope the explanation is useful.

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To find the possible lengths of the other two sides of triangle B, we can use the properties of similar triangles. Since triangle B is similar to triangle A, the corresponding sides are proportional.

The ratio of corresponding sides of similar triangles is constant. Let's denote the length of the unknown side in triangle B as x. We can set up the proportion:

( \frac{2}{5} = \frac{3}{x} = \frac{4}{\text{other side of triangle B}} )

From the given information, we know that the side lengths of triangle A are 2, 3, and 4. Therefore, the possible lengths of the other two sides of triangle B can be found by solving the proportions:

( \frac{2}{5} = \frac{3}{x} )

( 2x = 15 )

( x = \frac{15}{2} = 7.5 )

Thus, one possible length of the other side of triangle B is 7.5.

Similarly,

( \frac{2}{5} = \frac{4}{\text{other side of triangle B}} )

( 4 \times 5 = 2 \times \text{other side of triangle B} )

( \text{other side of triangle B} = \frac{20}{2} = 10 )

Thus, another possible length of the other side of triangle B is 10. Therefore, the possible lengths of the other two sides of triangle B are 7.5 and 10.

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