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?

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Answer 1 · 2017-12-01T12:54:55

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

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

Then $\frac{a}{d} = \frac{b}{e} = \frac{c}{f}$ $a/d = b/e = c/f$
$a = 1, b = 4, c = 4$ $a = 1, b = 4, c = 4$

If $d = 3$ $d = 3$ , then
$\frac{1}{3} = \frac{4}{e} = \frac{4}{f}$ $1/3 = 4/e = 4/f$
$:. e = 12, f = 12$

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 1,41 ,4 , and 4 44 . Triangle B is similar to triangle A and has a side of length 3 33 . What are the possible lengths of the other two sides of triangle B?