Triangle A has sides of lengths 8 ,3 8,3, and 4 4. Triangle B is similar to triangle A and has a side of length 6 6. What are the possible lengths of the other two sides of triangle B?

1 Answer
Brenda W.
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/4A8=63=C4
    A would be 16 and C would be 8

  • If the 4 side became 6
    Q/8=R/3=6/4Q8=R3=64
    Q would be 12 and R would be 4.5

  • If the 8 side became 6
    6/8 = Y/3 = Z/468=Y3=Z4
    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.

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