Question

The length of a rectangular room is 6 units greater than its width. write an equation expressing the rectangular room's area, a, as a function of w.

Answer 1

Answer:a = w² + 6w

Step-by-step explanation:To express the area, a, of a rectangular room as a function of its width, w, we first need to understand the relationship between the length and width of the room.

According to the given information, the length of the room is 6 units greater than its width. This can be expressed as:

Length = Width + 6

Next, we need to remember that the area of a rectangle is calculated by multiplying its length by its width. So, the equation for the area of the rectangular room, a, can be written as:

a = Length × Width

Substituting the expression for the length in terms of the width, we get:

a = (Width + 6) × Width

To simplify the equation, we can distribute the Width across the parentheses:

a = Width × Width + 6 × Width

Simplifying further, we have:

a = Width² + 6 × Width

So, the equation expressing the rectangular room's area, a, as a function of its width, w, is:

a = w² + 6w

In this equation, the area of the room is dependent on the width. By plugging in different values for the width, you can find the corresponding area of the room.

Answer 2

To express the rectangular room's area as a function of its width, use the formula A = length × width and substitute the given information.

Step-by-step explanation:

To express the rectangular room's area, a, as a function of its width, w, we can use the information given that the length of the room is 6 units greater than its width.

Let's assume the width is w, so the length will be w + 6.

The area of a rectangle is given by the formula: A = length × width. Substituting the values, we get a = (w + 6) × w.

This equation expresses the rectangular room's area as a function of its width.