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.

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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