# Triangle A has sides of lengths 7 ,4 , and 5 . Triangle B is similar to triangle A and has a side of length 3 . What are the possible lengths of the other two sides of triangle B?

Dec 10, 2017

A: Possible lengths of other two sides are $3 \frac{3}{4} , 5 \frac{1}{4}$
B: Possible lengths of other two sides are $2 \frac{2}{5} , 4 \frac{1}{5}$
C.Possible lengths of other two sides are $1 \frac{5}{7} , 2 \frac{1}{7}$

#### Explanation:

Side lengths of Triangle $A$ are $4 , 5 , 7$ according to size

A:
When side length $s = 3$ is smallest in similar triangle $B$

Then middle side length is $m = 5 \cdot \frac{3}{4} = \frac{15}{4} = 3 \frac{3}{4}$

Then largest side length is $m = 7 \cdot \frac{3}{4} = \frac{21}{4} = 5 \frac{1}{4}$

Possible lengths of other two sides are $3 \frac{3}{4} , 5 \frac{1}{4}$

B:
When side length $s = 3$ is middle one in similar triangle $B$

Then smallest side length is $m = 4 \cdot \frac{3}{5} = \frac{12}{5} = 2 \frac{2}{5}$

Then largest side length is $m = 7 \cdot \frac{3}{5} = \frac{21}{5} = 4 \frac{1}{5}$

Possible lengths of other two sides are $2 \frac{2}{5} , 4 \frac{1}{5}$

C:
When side length $s = 3$ is largest one in similar triangle $B$

Then smallest side length is $m = 4 \cdot \frac{3}{7} = \frac{12}{7} = 1 \frac{5}{7}$

Then middle side length is $m = 5 \cdot \frac{3}{7} = \frac{15}{7} = 2 \frac{1}{7}$

Possible lengths of other two sides are $1 \frac{5}{7} , 2 \frac{1}{7}$

A: Possible lengths of other two sides are $3 \frac{3}{4} , 5 \frac{1}{4}$ units
B: Possible lengths of other two sides are $2 \frac{2}{5} , 4 \frac{1}{5}$ units
C.Possible lengths of other two sides are $1 \frac{5}{7} , 2 \frac{1}{7}$ units
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