Question

Triangle A has sides of lengths `36`, `48`, and `18`. 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

`(3,4,3/2),(9/4,3,9/8),(6,8,3)`

Explanation:

Any of the 3 sides of triangle B could be of length 3 hence there are 3 different possibilities for the sides of B.

Since the triangles are similar then the `color(blue)"ratios of corresponding sides are equal"`

Let the 3 sides of triangle B be a ,b and c, corresponding to the sides 36 ,48 and 18 in triangle A.
`color(blue)"-------------------------------------------------------------------"`
If side a = 3 then ratio of corresponding sides `=3/36=1/12`

hence side b `=48xx1/12=4" and side c" =18xx1/12=3/2`

The 3 sides of B would be `(3,color(red)(4),color(red)(3/2))`
`color(blue)"----------------------------------------------------------------------"`
If side b = 3 then ratio of corresponding sides `3/48=1/16`

a `=36xx1/16=9/4" and side c" =18xx1/16=9/8`

The 3 sides of B would be `=(color(red)(9/4),3,color(red)(9/8))`
`color(blue)"-----------------------------------------------------------------------"`
If side c = 3 then ratio of corresponding sides `=3/18=1/6`

hence `a=36xx1/6=6" and b" =48xx1/6=8`

The 3 sides of B would be `=(color(red)(6),color(red)(8),3)`
`color(blue)"-------------------------------------------------------------------------"`