Question

Express the given quantity in terms of the indicated variable. The perimeter (in cm) of a rectangle that is 5 cm longer than it is wide; w = width of the rectangle (in cm).

Answer 1

The perimeter P of a rectangle when it is 5 cm longer than it is wide is expressed as P = 4w + 10 cm, where w is the width of the rectangle.

Step-by-step explanation:

To express the perimeter of a rectangle in terms of the width when the rectangle is 5 cm longer than it is wide, we start by defining the variables. Let w represent the width of the rectangle in cm. Then, the length L of the rectangle would be w + 5 cm, since it is given that the rectangle is 5 cm longer than it is wide. The perimeter of a rectangle is calculated by adding together the lengths of all four sides, which can be expressed as:

Perimeter = 2 × Width + 2 × Length

Substituting the variables and expression for the length we get:

Perimeter = 2 × w + 2 × (w + 5)

Expanding the equation:

Perimeter = 2w + 2w + 10

Combine like terms:

Perimeter = 4w + 10

Thus, the perimeter P of the rectangle in terms of the width w is P = 4w + 10 cm.