5. Rebecca would like to paint a wall in her bedroom and needs to figure out how much paint to buy. The height and length of the wall can be represented by the following diagram. [5 marks] a. Find an algebraic expression to represent the area of the wall. [ 2 marks] b. Find the actual area if $x=3 \mathrm{ft}$. [ 2 marks] c. Determine the cost if paint costs $\$ 0.75$ per $\mathrm{ft}^{2}$. [1 mark]

Step 1 ：First, we need to find an algebraic expression to represent the area of the wall. The area of a rectangle is given by the formula \(Area = length \times width\). In this case, the length of the wall is \(5x+4\) feet and the width is \(3x+2\) feet. So, the area of the wall can be represented by the expression \((5x+4)(3x+2)\) square feet.

Step 2 ：Next, we need to find the actual area of the wall when \(x=3\) feet. Substituting \(x=3\) into the expression for the area, we get \((5(3)+4)(3(3)+2) = (15+4)(9+2) = 19 \times 11 = 209\) square feet.

Step 3 ：Finally, we need to determine the cost of the paint. Given that paint costs $0.75 per square foot, the total cost of the paint will be \(209 \times 0.75 = \$156.75\).

Step 4 ：So, the algebraic expression to represent the area of the wall is \(\boxed{(5x+4)(3x+2)}\) square feet, the actual area of the wall when \(x=3\) feet is \(\boxed{209}\) square feet, and the cost of the paint is \(\boxed{\$156.75}\).