# 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?

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
$\frac{A}{8} = \frac{6}{3} = \frac{C}{4}$
A would be 16 and C would be 8

• If the 4 side became 6
$\frac{Q}{8} = \frac{R}{3} = \frac{6}{4}$
Q would be 12 and R would be 4.5

• If the 8 side became 6
$\frac{6}{8} = \frac{Y}{3} = \frac{Z}{4}$
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.