Question

The perimeter of a rectangle is 54 cm. If the length is 2 cm more than a number, and the width is 5 cm less than twice the same number, what is the number?

Answer 1

To find the unknown number based on the perimeter of a rectangle whose dimensions are algebraically linked to that number, you set up the perimeter equation, substitute in the expressions for length and width, and solve for the unknown number. In this case, the number is found to be 10.

Step-by-step explanation:

The student is asked to find a specific number based on information about the perimeter of a rectangle and algebraic expressions for its length and width. The length (L) is described as 2 cm more than an unknown number 'n,' and the width (W) is 5 cm less than twice the same number 'n.'

The formula for the perimeter (P) of a rectangle is P = 2L + 2W. Substituting the terms for L and W given in the question and the provided perimeter value:
54 = 2(n + 2) + 2(2n - 5)

Solving for 'n' involves expanding the equation, combining like terms, and then isolating 'n' on one side of the equation:

1. 54 = 2n + 4 + 4n - 10
2. 54 = 6n - 6
3. 60 = 6n
4. n = 10

So, the unknown number n is 10.