SOLUTION: I don't know how to solve this. The lengths of three sides of a triangle ABC are 6 centimeters, 4 centimeters, and 9 centimeters. Triangle DEF is similar to triangle ABC. The le

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Question 289251: I don't know how to solve this.
The lengths of three sides of a triangle ABC are 6 centimeters, 4 centimeters, and 9 centimeters. Triangle DEF is similar to triangle ABC. The length of one of the sides of triangle DEF is 36 centimeters. What is the greatest perimeter possible for triangle DEF?
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
You know the ratio of the sides of the first triangle.
You know that similar triangles will have the same ratio on its sides.
So, to get the largest perimeter, then you need to make the smallest side of the second triangle be 36 (so the other sides are longer)
So the smallest side of the first triangle is 4. The smallest side fo the second triangle is 36. That's a factor of 9.
Each of the other sides of the larger triangle will be 9 times the similar side of the smaller one.
6*9 = 54
9*9 = 81
So the perimeter is
Make sense