A triangle has sides measuring 10, 14, and 18. A similar triangle has its largest side measuring 54. What is the perimeter of the similar triangle?

It was clearly stated that the two triangles are similar figures. Therefore, the ratio between the corresponding legs is the same.

Getting the ratio of two largest sides is below:

R=54/18

R=3

Solving the next missing side (let "b" represent the second missing side) using the value of R.

R=b/14, 3=b/14 and therefore b is equal to 42.

Solving the next missing side (let "a" represent the second missing side) using the value of R.

R=a/10, 3=b/10 and therefore b is equal to 30.

We have the three sides of the second triangle. Then we can solve for the perimeter using formula P=a+b+c. The solution is P=54+42+30 and answer is 126.