# 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.

Mar 22, 2018

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:

$A = l w = \left(w + 7\right) w = {w}^{2} + 7 w$

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 $w = 12$:

$A = {w}^{2} + 7 w = {12}^{2} + 7 \times 12 = 144 + 84 = 228$ units