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
