Write a function rule for the area of a rectangle whose length is 5 ft more than its width. What is the area of the rectangle when its width is 11 ft?
Write a function for the area A of the rectangle using the independent variable width W.
To write the function rule for the area of a rectangle, we need to determine the relationship between the length and width.
Given that the length is 5 ft longer than the width, we can express the length as (W + 5), where W is the width.
The formula for the area of a rectangle is A = length × width.
Substituting the length and width values, we have A = (W + 5) × W.
Simplifying the equation, we get A = W^2 + 5W.
This is the function rule for the area of the rectangle in terms of the width.
To find the area of the rectangle when the width is 11 ft, we substitute W = 11 into the function.
A = 11^2 + 5(11)
A = 121 + 55
A = 176
Therefore, the area of the rectangle when the width is 11 ft is 176 square feet.
To write a function rule for the area of a rectangle, you need to express the area in terms of the independent variable, which in this case is the width (W) of the rectangle.
Let's start by defining the width as W. According to the problem, the length of the rectangle is 5 feet more than its width. So, the length can be expressed as W + 5.
The formula for calculating the area of a rectangle is:
Area = Length × Width
Substituting the values we have, we get:
Area = (W + 5) × W
Simplifying this expression, we get:
Area = W^2 + 5W
Hence, the function rule for the area of the rectangle in terms of the width is:
A(W) = W^2 + 5W
Now, to find the area of the rectangle when the width is 11 feet, we can substitute 11 for W in the function:
A(11) = (11)^2 + 5(11)
Calculating this expression, we get:
A(11) = 121 + 55
A(11) = 176
Therefore, the area of the rectangle when the width is 11 feet is 176 square feet.
A = L w
but L = w+5
so
A = (w+5)w = w^2 + 5 w
if w = 11
A = 11^2 + 5(11) = 121+55 = 176