Final answer:
To solve this problem, we use the Pythagorean theorem to find the original lengths of the sides of the right triangle.
Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's denote the length of the smaller side as a, the length of the larger side as b, and the length of the hypotenuse as c.
a² + b² = c²
From the given information, we have c = 3√5. Substituting this into the equation, we get:
a² + b² = (3√5)²
Simplifying further:
a² + b² = 45
Now, let's consider the new triangle formed by tripling the smaller side and doubling the larger side. The length of the new hypotenuse, denoted as d, is given as d = 15. Using the same equation, we can write:
(3a)² + (2b)² = 225
Simplifying this equation:
9a² + 4b² = 225
Now, we have two equations:
a² + b² = 459a² + 4b² = 225
To solve this system of equations, we can use substitution, elimination, or matrices. Once we find the values of a and b, we can calculate the lengths of the sides of the original triangle.