Question

the length of a rectangle is 4 more than the width. the area of the rectangle is 60 square yards. what is the length of the rectangle? let w = width and 4 + w = length. which equation represents the situation? √ w(4 +w) = 60 complete using the zero product property, the equation is . (w - 10)(w - 6) = 0 (w - 10)(w + 6) = 0 (w + 10)(w - 6) = 0 (w + 10)(w + 6) = 0

Explanation:

Step1: Expand the area equation

We know the area equation is \( w(4 + w)=60 \). Expand it: \( w^{2}+4w = 60 \), then rearrange to standard quadratic form: \( w^{2}+4w - 60=0 \).

Step2: Factor the quadratic equation

We need two numbers that multiply to \(- 60\) and add to \(4\). The numbers are \(10\) and \(- 6\) (since \(10\times(-6)=-60\) and \(10+(-6) = 4\)). So the factored form is \((w + 10)(w-6)=0\).

Step3: Solve for width

Set each factor equal to zero: \(w + 10=0\) gives \(w=- 10\) (discard, width can't be negative), \(w - 6=0\) gives \(w = 6\).

Step4: Find the length

Length is \(w + 4\), substitute \(w = 6\): \(6+4=10\) yards.

Answer:

The equation using zero product property is \((w + 10)(w - 6)=0\), and the length of the rectangle is 10 yards.