Triangle A has sides of lengths $7 ,4$ , and $8$ . Triangle B is similar to triangle A and has a side of length $9$ . What are the possible lengths of the other two sides of triangle B?

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Answer 1 · 2017-12-07T14:46:39

Possible lengths of the triangle B are

Case (1)
$9, 15.75, 18$

Case (2)
$9, 5.14, 10.29$

Case (3)
$9, 4.5, 7.875$

Triangles A & B are similar.
Case (1)
$:.9/4=b/7=c/8$
$b=(9*7)/4= 15.75$
$c=(9*8)/4= 18$

Possible lengths of other two sides of triangle B are
$9, 15.75, 18$

Case (2)
$:.9/7=b/4=c/8$
$b=(9*4)/7=5.14$
$c=(9*8)/7=10.29$

Possible lengths of other two sides of triangle B are
$9, 5.14, 10.29$

Case (3)
$:.9/8=b/4=c/7$
$b=(9*4)/8=4.5$
$c=(9*7)/8=7.875$

Possible lengths of other two sides of triangle B are
$9, 4.5, 7.875$

Triangle A has sides of lengths 7 ,4 7 ,4 , and 8 8 . Triangle B is similar to triangle A and has a side of length 9 9 . What are the possible lengths of the other two sides of triangle B?