Write a function rule for the area of a rectangle whose length is 6 ft more than its width. What is the area of the rectangle when its width is 7 ft? Write a function for the area A of the rectangle using the independent variable-width W.
The expression for the area in terms of the width is: A = w 2 + 7 w When w = 12 , the area is 228 units. Explanation: We know that the formula for the area of a rectangle is: Area = length x width A = l w In this specific case, though, we are told that the length is 7 units greater than the width: l = w + 7 We can substitute this value for l into our area formula, and then there will be only one variable on the right-hand side: A = l w = ( w + 7 ) w = w 2 + 7 w This expression is the answer to the final sentence in the question, asking us to write an expression for A in terms only of w . Now we can use our expression to find the area in the situation where w = 12 : A = w 2 + 7 w = 12 2 + 7 × 12 = 144 + 84 = 228 units
