Question

Triangle A has sides of lengths `24`, `16`, and `18`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the possible lengths of the other two sides of triangle B?

Answer 1

`(16,32/3,12),(24,16,18),(64/3,128/9,16)`

Explanation:

Anyone of the 3 sides of triangle B could be of length 16 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"`

Name the 3 sides of triangle B- a , b and c to correspond with the sides- 24 , 16 and 18 in triangle A.
`color(blue)"-------------------------------------------------------------"`
If side a = 16 then ratio of corresponding sides `=16/24=2/3`

and side b `= 16xx2/3=32/3," side c" = 18xx2/3=12`

The 3 sides of B would be `(16,color(red)(32/3),color(red)(12))`
`color(blue)"----------------------------------------------------------------"`
If side b = 16 then ratio of corresponding sides `=16/16=1`
and side a `=24", side c"=18`

The 3 sides of B would be `(color(red)(24),16,color(red)(18))`
`color(blue)"-----------------------------------------------------------------"`

If side c = 16 then ratio of corresponding sides `=16/18=8/9`

and side a `=24xx8/9=64/3," side b" =16xx8/9=128/9`

The 3 sides of B would be `(color(red)(64/3),color(red)(128/9),16)`
`color(blue)"-------------------------------------------------------------------"`