6. A carpenter is installing a countertop with an area of $x^{2}+7 x+6$. [6 marks] a. Write expressions for the length and width of the countertop. [3 marks] b. What is the shape of the countertop. [1 mark] c. Calculate the area of the countertop if $x=1 \mathrm{ft}$. Include units. [ 2 marks]

Step 1 ：The question is asking for expressions for the length and width of the countertop. Since the area of a rectangle is given by the product of its length and width, we can express the area as a product of two binomials.

Step 2 ：We can factor the quadratic expression \(x^{2}+7 x+6\) to find these expressions.

Step 3 ：The expressions for the length and width of the countertop are \(x+1\) and \(x+6\).

Step 4 ：Final Answer: The expressions for the length and width of the countertop are \(\boxed{x+1}\) and \(\boxed{x+6}\).