Question

the length of a rectangle is 8 more than the width. the area is 84 square centimeters. find the length and width of the rectangle. answer how to enter your answer (opens in new window) width = centimeters length = centimeters

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ cm. Then the length is $(x + 8)$ cm.

Step2: Set up area - equation

The area formula of a rectangle is $A=\text{length}\times\text{width}$. So we have $x(x + 8)=84$.

Step3: Expand and rearrange

Expand the left - hand side: $x^{2}+8x=84$. Rearrange to get a quadratic equation: $x^{2}+8x - 84 = 0$.

Step4: Factor the quadratic equation

Factor $x^{2}+8x - 84$ as $(x + 14)(x - 6)=0$.

Step5: Solve for $x$

Set each factor equal to zero: $x+14 = 0$ gives $x=-14$; $x - 6=0$ gives $x = 6$. Since the width cannot be negative, we take $x = 6$.

Step6: Find the length

The length is $x + 8$. Substitute $x = 6$ into it, we get the length is $6 + 8=14$ cm.

Answer:

Width = 6 centimeters
Length = 14 centimeters