Question

Triangle A has sides of lengths `18`, `24`, and `12`. Triangle B is similar to triangle A and has a side of length `7`. What are the possible lengths of the other two sides of triangle B?

Answer 1

`(7,28/3,14/3),(21/4,7,7/2),(21/2,14,7)`

Explanation:

Anyone of the 3 sides of triangle B could be of length 7, 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- 18 , 24 and 12 in triangle A.
`color(blue)"-------------------------------------------------------"`
If side a = 7 then ratio of corresponding sides `=7/18`

and side b `=24xx7/18=28/3," side c " =12xx7/18=14/3`

The 3 sides of B would be `(7,color(red)(28/3),color(red)(14/3))`
`color(blue)"--------------------------------------------------------------"`

If side b = 7 then ratio of corresponding sides `=7/24`

and side a `=18xx7/24=21/4," side c " =12xx7/24=7/2`

The 3 sides of B would be `(color(red)(21/4),7,color(red)(7/2))`
`color(blue)"-------------------------------------------------------------------"`

If side c = 7 then ratio of corresponding sides `=7/12`

and side a `=18xx7/12=21/2," side b " =24xx7/12=14`

The 3 sides of B would be `(color(red)(21/2),color(red)(14),7)`
`color(blue)"--------------------------------------------------------------------"`