Final answer:
To find the lengths of the sides of a right-angled triangle when the legs are 2 cm and 4 cm shorter than the hypotenuse, we use the Pythagorean theorem to set up an equation and solve for the length of the shortest side (a). Subsequently, the lengths of the other sides can be found.
Step-by-step explanation:
The question requires the application of the Pythagorean theorem to find the lengths of the sides of a right-angled triangle where the sides containing the right angle are shorter than the hypotenuse by 2 cm and 4 cm respectively. Let's set the length of one side of the triangle as a cm. According to the problem, the second side would then be a + 2 cm, and the hypotenuse would be a + 4 cm. By the Pythagorean theorem, which states that in a right-angled triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), we can write the equation:
a^2 + (a + 2)^2 = (a + 4)^2
By expanding and simplifying this equation, we can solve for a. Once a is determined, we can also find the lengths of the other two sides of the triangle.