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Triangle A has sides of lengths #5 ,4 #, 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?

Answer 1

Claire Akin

Possible lengths of other two sides are
Case 1 : 1.25, 2
Case 2 : 0.8, 1.6
Case 3 : 0.5, 0.625

Triangles A & B are similar. Case (1) #:.1/4=b/5=c/8# #b=(1*5)/4= 1.25# #c=(1*8)/4= 2#

Possible lengths of other two sides of triangle B are #9, 1.25, 2#

Case (2) #:.1/5=b/4=c/8# #b=(1*4)/5=0.8# #c=(1 * 8)/5=1.6#

Possible lengths of other two sides of triangle B are #9, 0.8, 1.6#

Case (3) #:.1 /8=b/4=c/5# #b=(1*4)/8=0.5# #c=(1*5)/8=0.625#

Possible lengths of other two sides of triangle B are #8, 0.5, 0.625#

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Answer 2

Sadie Adams

Since triangle B is similar to triangle A, the ratios of corresponding sides are equal. Let's denote the lengths of the corresponding sides of triangle B as ( x ) and ( y ). Then, we have the following ratios:

[ \frac{x}{5} = \frac{1}{4} \quad \text{and} \quad \frac{y}{8} = \frac{1}{4} ]

Solving these ratios, we find:

[ x = \frac{5}{4} \quad \text{and} \quad y = 2 ]

So, the possible lengths of the other two sides of triangle B are ( \frac{5}{4} ) and 2.

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