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: Set up area - equation

The area formula for a rectangle is $A = length\times width$. Given $width = w$ and $length=w + 4$, and $A = 60$. So the equation is $w(w + 4)=60$. Expanding it gives $w^{2}+4w-60 = 0$.

Step2: Factor the quadratic equation

We factor $w^{2}+4w - 60=0$. We need to find two numbers that multiply to - 60 and add up to 4. The numbers are 10 and - 6. So, $w^{2}+4w-60=(w + 10)(w - 6)=0$.

Step3: Use the zero - product property

According to the zero - product property, if $ab = 0$, then either $a = 0$ or $b = 0$. So, $w+10 = 0$ or $w - 6=0$. Solving for $w$, we get $w=-10$ or $w = 6$. Since the width cannot be negative, $w = 6$.

Step4: Find the length

Since the length $l=w + 4$, substituting $w = 6$ into the length formula, we get $l=6 + 4=10$.

Answer:

10 yards