The sides of a triangle measure 9 , 15 , and 18 . If the shortest side of a similar triangle measures 6 , find the length of the longest side of this triangle .
a . 5
b . 10
c. 12
d . 15
The answer is c.12
To find the length of the longest side of a similar triangle, you can use the concept of similarity ratios.
In this case, we have two triangles: one with sides measuring 9, 15, and 18; and the other with an unknown length for the longest side.
The similarity ratio between the two triangles is found by comparing the corresponding sides. In this case, the shortest side of the first triangle is 9 and the shortest side of the second triangle is 6. Therefore, the similarity ratio would be 6/9.
To find the length of the longest side of the second triangle, we can multiply the length of the longest side of the first triangle by the similarity ratio. The longest side of the first triangle is 18, so the length of the longest side of the second triangle would be:
(18) x (6/9) = 12
Therefore, the length of the longest side of the similar triangle with the shortest side measuring 6 is 12.
Therefore, the correct answer is option c. 12.