Triangle dimensions.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.
We know that the corresponding sides of the two triangles must be proportional. Therefore, we know that the proportion 9:6 will hold for all of the sides.
For the longest side of the second triangle, we use the following equation:
9/6 = 18/x
Now we cross multiply to find for x.
9x = 108 or x = 12
So the length of the longest side of the second triangle is 12 units.
The ratio of sides of the first triangle is 9:15:18.
The ratio of sides of the similar triangle is 6:X:Y.
Now, we'll determine the proportion:
6/9 = a
We'll cross multiply and we'll get:
9a = 6
We'll divide by 3:
3a = 2
a = 2/3
We'll multiply each known length of the side by the proportion a:
9*(2/3) = 6
15*(2/3) = 10
18*(2/3) = 12
The length of the longest side of the triangle is of 12 units.