A triangle whose sides are 5, 12, and 13 inches is similar to a triangle whose longest side is 39 inches. What is the perimeter of the larger triangle?
39/13 = 3 making the sides of the larger similar triangle 10, 36 and 39 for a perimeter of 85.
To find the perimeter of the larger triangle, we need to determine the ratio between the sides of the two triangles.
In this case, the given triangle has sides of lengths 5, 12, and 13 inches. These sides form a Pythagorean triple, which means it is a right triangle.
The larger triangle is similar to the given triangle, which means the corresponding sides are proportional. We can use the ratio of the longest sides to find the scaling factor.
Let's set up the proportion:
(original longest side) / (given longest side) = (original perimeter) / (given perimeter)
The original longest side is 13 inches, and the given longest side is 39 inches:
13 / 39 = (original perimeter) / (given perimeter)
Simplifying the equation:
1 / 3 = (original perimeter) / (given perimeter)
We can solve for the original perimeter by multiplying both sides of the equation by the given perimeter:
original perimeter = (original longest side) * (given perimeter) / (given longest side)
Substituting the known values:
original perimeter = 13 * 39 / 39 = 13 inches
Therefore, the perimeter of the larger triangle is 13 inches.