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?

1 Answer
Binayaka C.
Dec 10, 2017

A: Possible lengths of other two sides are #3 3/4 , 5 1/4#
B: Possible lengths of other two sides are #2 2/5 , 4 1/5#
C.Possible lengths of other two sides are #1 5/7 , 2 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*3/4=15/4=3 3/4#

Then largest side length is #m=7*3/4=21/4 = 5 1/4#

Possible lengths of other two sides are #3 3/4 , 5 1/4#

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

Then smallest side length is #m=4*3/5=12/5=2 2/5#

Then largest side length is #m=7*3/5=21/5 = 4 1/5#

Possible lengths of other two sides are #2 2/5 , 4 1/5#

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

Then smallest side length is #m=4*3/7=12/7=1 5/7#

Then middle side length is #m=5*3/7=15/7 = 2 1/7#

Possible lengths of other two sides are #1 5/7 , 2 1/7#

A: Possible lengths of other two sides are #3 3/4 , 5 1/4# units
B: Possible lengths of other two sides are #2 2/5 , 4 1/5# units
C.Possible lengths of other two sides are #1 5/7 , 2 1/7# units
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