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? using the zero product property, the equation is what is the length of the rectangle? 10 yards

Explanation:

Step1: Define variables and area formula

Let \( w \) be the width, length \( l = w + 4 \). Area of rectangle: \( A = l \times w \). Given \( A = 60 \), so \( w(w + 4)=60 \).

Step2: Form quadratic equation

Expand: \( w^2 + 4w - 60 = 0 \). Factor: \( (w + 10)(w - 6)=0 \).

Step3: Solve for width

Using zero - product property, \( w + 10 = 0 \) (rejected, width can't be negative) or \( w - 6 = 0 \), so \( w = 6 \).

Step4: Find length

Length \( l = w + 4 = 6 + 4 = 10 \).

Answer:

The length of the rectangle is 10 yards. The equation representing the situation is \( w(w + 4)=60 \) (or \( w^2+4w - 60 = 0 \)), and using zero - product property, we solve \( (w + 10)(w - 6)=0 \) to get the length.