Question

a window is in the shape of a rectangle with dimensions as shown.
match each question to the expression that answers it. some expressions will not be used.
which expression represents the area of the window?
which expression represents the perimeter of the window?

Explanation:

Step 1: Find the area of the rectangle

The area \(A\) of a rectangle is given by \(A = \text{length}\times\text{width}\). Here, length \(l=x^{2}+3x - 4\) and width \(w=x + 3\).
Using the distributive property (also known as the FOIL method for binomials, but extended for polynomials):

$$
LATEXBLOCK0
$$

Step 2: Find the perimeter of the rectangle

The perimeter \(P\) of a rectangle is given by \(P=2(\text{length}+\text{width})\).
Substitute length \(l=x^{2}+3x - 4\) and width \(w=x + 3\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

• Area of the window: \(x^{3}+6x^{2}+5x - 12\)
• Perimeter of the window: \(2x^{2}+8x-2\)