Final answer:
The dimensions of the rectangle are Length = 3 cm and Width = 4 cm.
Step-by-step explanation:
To solve this problem, let's assume the length of the rectangle is 'x' centimeters.
According to the given information, the width is 1 centimeter more than the length, so the width is 'x + 1' centimeters.
The diagonal is 2 centimeters longer than the length, so the diagonal is 'x + 2' centimeters.
Using the Pythagorean theorem for a right triangle (where the length, width, and diagonal form the sides of the triangle), we have:
x2 + (x + 1)2 = (x + 2)2
Simplifying this equation, we get:
x2 + x2 + 2x + 1 = x2 + 4x + 4
Combining like terms, we have:
2x2 + 2x + 1 = x2 + 4x + 4
x2 - 2x - 3 = 0
Factoring or using the quadratic formula, we find that x = 3 or x = -1.5. Since the length cannot be negative, we take x = 3. Therefore, the length of the rectangle is 3 centimeters and the width is 3 + 1 = 4 centimeters.