Final answer:
To find the missing sides of a right triangle with a given shortest side and the difference between the other two sides, we can use the Pythagorean theorem. Applying the theorem, we find that the missing sides are 8 and 10 centimeters long.
Step-by-step explanation:
To find the missing sides of a right triangle, we can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the shortest side is given as 6 centimeters. Let's assume that the other two sides are 'a' and 'a+2' centimeters long. Applying the Pythagorean theorem, we have:
6² + a² = (a+2)²
Simplifying this equation, we get:
36 + a² = a² + 4a + 4
By canceling out the common terms, we find:
36 = 4a + 4
Subtracting 4 from both sides, we have:
32 = 4a
Finally, dividing both sides by 4, we get:
a = 8
So, the missing sides are 8 and 10 centimeters.