Question

let w = width and 4 + w = length. which equation represents the situation? using the zero product property, the equation is what is the length of the rectangle? 10 yards

Explanation:

1. Assume a relationship (for example, area of a rectangle):

• Let's assume the area of the rectangle \(A\) is given (not given in the problem - but if we assume \(A\) is known). The area of a rectangle is \(A=\text{length}\times\text{width}\). Given \(\text{width}=w\) and \(\text{length}=4 + w\), the equation representing the situation (if area \(A\) is known) is \(A=w(4 + w)=w^{2}+4w\). If we assume the area \(A = 60\) (for example, to show the zero - product property application), then \(w^{2}+4w-60 = 0\).

Step1: Set up the area equation

If the area of the rectangle is \(A\), then \(A=w(4 + w)\), which expands to \(A=w^{2}+4w\). If we assume \(A = 60\) (a made - up value to complete the zero - product property step), we get \(w^{2}+4w-60=0\).

Step2: Factor the quadratic equation

We factor \(w^{2}+4w - 60=(w + 10)(w - 6)=0\).

Step3: Apply the zero - product property

If \((w + 10)(w - 6)=0\), then either \(w+10 = 0\) or \(w - 6=0\). So \(w=-10\) or \(w = 6\). Since width cannot be negative, \(w = 6\).

Step4: Find the length

Since length \(l=4 + w\) and \(w = 6\), then \(l=4+6 = 10\).

Answer:

The equation representing the situation (assuming area \(A\)) is \(A=w(4 + w)\) (or if \(A = 60\), \(w^{2}+4w-60 = 0\)). The factored form for zero - product property application (when \(A = 60\)) is \((w + 10)(w - 6)=0\). The length of the rectangle is \(10\) yards.