Final answer:
To find the number, set up an equation using the given information. Solve for x by simplifying the equation, combining like terms, and dividing.
Step-by-step explanation:
To find the number, we can set up an equation using the given information and solve for the unknown. Let's let the number be x. According to the problem, the length of the rectangle is 2cm more than the number, so the length is x + 2. The width is 5cm less than twice the same number, so the width is 2x - 5. The perimeter of the rectangle is the sum of the lengths of all four sides, so we can set up the equation: 2(x + 2) + 2(2x - 5) = 54. Simplifying the equation, we get: 2x + 4 + 4x - 10 = 54. Combining like terms, we have: 6x - 6 = 54. Adding 6 to both sides, we get: 6x = 60. Dividing both sides by 6, we find: x = 10.
Therefore, the number is 10.