Question

Triangle A has sides of lengths `48 ,24`, and `54`. Triangle B is similar to triangle A and has a side of length `5`. What are the possible lengths of the other two sides of triangle B?

Answer 1

several possibilities. See explanation.

Explanation:

We know, if `a,b,c` represent the sides of a triangle, then a similar triangle will have side given by `a',b',c'` that follows:

`a/(a')=b/(b')=c/(c')`

Now, let `a=48," " b=24 " and "c=54`

There are three possibilities:

• Case I: `a' = 5`

so, `b' = 24xx5/48 = 5/2`

and, `c' = 54xx5/48 = 45/8`

• Case II: `b' = 5`

so, `a' = 48xx5/24 = 10`

and, `c' = 54xx5/24 = 45/4`

• Case III: `c' = 5`

so, `a' = 48xx5/54 = 40/9`

and, `b' = 24xx5/54 = 20/9`