Triangle A has sides of lengths #8 ,3 #, and #4 #. Triangle B is similar to triangle A and has a side of length #6 #. What are the possible lengths of the other two sides of triangle B?
1 Answer
Mar 2, 2016
Triangle A is impossible, but theoretically it would be 16, 6, 8 and 12, 4.5, 6 and 6, 2.25, 3
Explanation:
Since a property of all triangles is that any two sides of a triangle added together are greater than the remaining side. Since 3 + 4 is less than 8 Triangle A is non existent.
However, if this was possible it would depend in which side it corresponds with.

If the 3 side became 6
#A/8=6/3=C/4#
A would be 16 and C would be 8 
If the 4 side became 6
#Q/8=R/3=6/4#
Q would be 12 and R would be 4.5 
If the 8 side became 6
#6/8 = Y/3 = Z/4#
Y would be as 2.25 and Z would be 3
All of these happen because when two shapes are similar all of the sides are drawn proportionally to the original figure so you have to scale each side accordingly.