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?

May 1, 2016

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:

$\frac{a}{a '} = \frac{b}{b '} = \frac{c}{c '}$

Now, let $a = 48 , \text{ " b=24 " and } c = 54$

There are three possibilities:

• Case I: $a ' = 5$

so, $b ' = 24 \times \frac{5}{48} = \frac{5}{2}$

and, $c ' = 54 \times \frac{5}{48} = \frac{45}{8}$

• Case II: $b ' = 5$

so, $a ' = 48 \times \frac{5}{24} = 10$

and, $c ' = 54 \times \frac{5}{24} = \frac{45}{4}$

• Case III: $c ' = 5$

so, $a ' = 48 \times \frac{5}{54} = \frac{40}{9}$

and, $b ' = 24 \times \frac{5}{54} = \frac{20}{9}$