Write a function rule for the area of a rectangle whose length is 7 ft more than its width. What is the area of the rectangle when its width is 12 ​ft? Write a function for the area A of the rectangle using the independent variable width W.

1 Answer
Mar 22, 2018

Answer:

The expression for the area in terms of the width is:

#A=w^2+7w#

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=lw#

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=lw=(w+7)w=w^2+7w#

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+7w=12^2+7xx12=144+84=228# units