Triangle A has sides of lengths $1 ,4$ , and $4$ . 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?

Question

3172 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-01T12:54:55

The possible lengths of the DEF triangle are
$color(red)(3,12,12 )$ & $color(blue)(3/4,3,3)$

Since the two triangles are similar, their corresponding sides are proportional.
Let the two triangles be ABC & DEF.

Then $a/d = b/e = c/f$
$a = 1, b = 4, c = 4$

If $d = 3$ , then
$1/3 = 4/e = 4/f$
$:. e = 12, f = 12$

If $e = 3$ , then
$4/3 = 1/d = 4/f$
$:. d = 3/4, f = 3$

The possible lengths of the DEF triangle are
$color(red)(3,12,12 )$ & $color(blue)(3/4,3,3)$

Triangle A has sides of lengths 1 ,4 1 ,4 , and 4 4 . Triangle B is similar to triangle A and has a side of length 3 3 . What are the possible lengths of the other two sides of triangle B?