Question

Triangle A has sides of lengths `12`, `9`, and `6`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the possible lengths of the other two sides of triangle B?

Answer 1

(16,12,8), (`64/3,16,32/3 ) , (32,24,16)`

Explanation:

Since the triangles are similar then the ratios of corresponding sides are equal.
Name the 3 sides of triangle B , a,b and c corresponding to the sides 12,9 and 6 in triangle A.
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If side a = 16 then ratio of corresponding sides `= 16/12 = 4/3`

hence `b = 9xx4/3 = 12" and " c = 6xx4/3 = 8`

The 3 sides of B = (16 , 12 , 8 )
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If side b = 16 then ratio of corresponding sides `= 16/9`

hence a =`12xx16/9 = 64/3" and " c = 6xx16/9 = 32/3`

The 3 sides of B `=(64/3 , 16 , 32/3 )`
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If c = 16 then ratio of corresponding sides = `16/6 = 8/3`

hence a`= 12xx8/3 = 32" and " b = 9xx8/3 = 24`

The 3 sides of B = (32 , 24 , 16 )
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