Then length of a rectangle is 5 less than 2 times the width, write a polynomial for the perimeter and a polynomial for the area.
The length of a rectangle is 5 inches less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.
width=w
length=2w-5
perimeter: 2(w+l) = 2(w+2w-5) = 2(3w-5) = 6w-15
area: wl = w(2w-5) = 2w^2-10w
that wasn't so hard, now, was it?
Math is one of my strongest subjects. :/
To write a polynomial for the perimeter of a rectangle, we need to find the expressions for the length and width.
Let's assume the width of the rectangle is 'w'. According to the given information, the length of the rectangle is 5 less than 2 times the width. In mathematical terms, we can represent the length as (2w - 5).
The formula for the perimeter of a rectangle is 2(length + width). Substituting the length and width expressions, we get:
Perimeter = 2((2w - 5) + w)
Simplifying further, we have:
Perimeter = 2(3w - 5)
Perimeter = 6w - 10
Therefore, the polynomial for the perimeter of the rectangle is 6w - 10.
To write a polynomial for the area of a rectangle, we use the formula A = length * width. Substituting the length and width expressions, we get:
Area = (2w - 5) * w
Expanding this, we have:
Area = 2w^2 - 5w
Therefore, the polynomial for the area of the rectangle is 2w^2 - 5w.