Question

the length of a rectangle is 4 units more than the width. the area of the rectangle is 45 square units. what is the width, in units, of the rectangle?

Explanation:

Step1: Set up variables

Let the width of the rectangle be \(x\) units. Then the length is \(x + 4\) units.

Step2: Use the area formula

The area of a rectangle is \(A=\text{length}\times\text{width}\). So \(x(x + 4)=45\).
Expanding gives \(x^{2}+4x-45 = 0\).

Step3: Factor the quadratic equation

We factor \(x^{2}+4x - 45\). We need two numbers that multiply to \(- 45\) and add up to \(4\). The numbers are \(9\) and \(-5\).
So \((x + 9)(x-5)=0\).

Step4: Solve for \(x\)

Using the zero - product property:
If \(x+9 = 0\), then \(x=-9\). But width cannot be negative.
If \(x - 5=0\), then \(x = 5\).

Answer:

\(5\)