Question

MULTIPLE CHOICE A rectangle has a length that is 2 inches longer than its width. The area of the rectangle is 48 square inches. What is the length of the rectangle?

F 48 in.

G 8 in.

H 6 in.

J 2 in.

Short answer

The length of the rectangle is 8 in.

Step-by-step solution

Step 1. Convert.

Convert given information in the equation form.

Let $I$and $w$be the length and width of the rectangle respectively, such that,

$l=2+w$

Step 2. Write the formula of the area of a rectangle.

The area of the rectangle is given by $A=l\times w$.

Replace $A$by 48 and $I$by $2+w$into $A=l\times w$.

$$\begin{gathered} \left(2+w\right)\times w=48 \\ {w}^2+2w=48 \end{gathered}$$

Step 3. Subtract.

Subtract from both sides of the given equation.

$$\begin{gathered} w^2+2w-48=48-48 \\ =0 \end{gathered}$$

Step 4. Factor by using GCF.

Factor by using GCF to get the form $xy=0$.

$\left(w+8\right)\left(w-6\right)=0$

Step 5. Apply zero product property.

Apply zero product property to the given equation, $\left(w+8\right)\left(w-6\right)=0$.

$$\begin{gathered} w+8=0\text{or}w-6=0 \\ \text{w}=-8w=6 \end{gathered}$$

As the value of length cannot be negative, therefore, the value of role="math" localid="1647952357609" $w$, that is, the width of the rectangle is 6 in.

Therefore, the length of a rectangle is 8 in and as option G completely matches with the obtained answer, option G is the correct answer.