Question

Marta created a rectangle where the length was five more than twice the width. She then determined that the area of the rectangle could be found by using the function A = 2w^2 +5w, where w is the width of the rectangle. If the area of the rectangle is 18 in², what is the width of the rectangle?

Answer 1

Width of the rectangle = 2 inches

Step-by-step explanation:

Given the equation of the area of the rectangle as;

`A=2w^2+5w`

Given A = 18 in^2, let's substitute the given value of A into the equation and solve for w;

`\begin{gathered} 18=2w^2+5w \\ 2w^2+5w-18=0 \end{gathered}`

Let's go ahead and solve the resulting quadratic equation following the below steps;

1. Look for two factors -36 (-18 x 2) whose sum will be 5.

The two factors are 9 and -4, let's go ahead and split the middle term as shown below;

`\begin{gathered} 2w^2+9w-4w-18=0 \\ w(2w+9)-2(2w+9)=0 \\ (w-2)(2w+9)=0 \end{gathered}`

2. Let's equate to zero and solve for w;

`\begin{gathered} w-2=0 \\ w=2in \\ \text{Also, } \\ 2w+9=0 \\ w=-(9)/(2) \end{gathered}`

We'll go with the positive value of w, so w = 2 inches