Question

Triangle A has sides of lengths `39`, `45`, and `27`. 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?

Answer 1

`(3,45/13,27/13),(13/5,3,9/5),(13/3,5,3)`

Explanation:

Since triangle B has 3 sides, anyone of them could be of length 3 and so there are 3 different possibilities.

Since the triangles are similar then the ratios of corresponding sides are equal.

Label the 3 sides of triangle B, a, b and c corresponding to the sides 39, 45 and 27 in triangle A.

`"--------------------------------------------------------------------------------"`
`"if a = 3 then ratio of corresponding sides "=3/39=1/13`

`rArrb=45xx1/13=45/13" and "c=27xx1/13=27/13`

`"the 3 sides of B"=(3,color(red)(45/13),color(red)(27/13))`
`"---------------------------------------------------------------------------------"`
`"if b = 3 then ratio of corresponding sides "=3/45=1/15`

`rArra=39xx1/15=13/5" and "c=27xx1/15=9/5`

`"the 3 sides of B "=(color(red)(13/5),3,color(red)(9/5))`
`"----------------------------------------------------------------------------"`
`"if c = 3 then ratio of corresponding sides "=3/27=1/9`

`rArra=39xx1/9=13/3" and " b=45xx1/9=5`

`"the 3 sides of B "=(color(red)(13/3),color(red)(5),3)`

`"-------------------------------------------------------------------------------"`