Question

the length of a rectangle is 9 more than the width. the area is 112 square centimeters. find the length and width of the rectangle. answerhow to enter your answer (opens in new window) 2 points width = centimeters length = centimeters

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ cm. Then the length is $(x + 9)$ cm.

Step2: Set up area - equation

The area of a rectangle is $A=\text{length}\times\text{width}$. So we have the equation $x(x + 9)=112$.
Expanding gives $x^{2}+9x - 112 = 0$.

Step3: Solve the quadratic equation

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 1$, $b = 9$, $c=-112$), we can use the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ or factor.
Factoring $x^{2}+9x - 112=(x + 16)(x - 7)=0$.
Setting each factor equal to zero gives $x+16 = 0$ or $x - 7=0$.
We get $x=-16$ or $x = 7$. Since the width cannot be negative, we take $x = 7$.

Step4: Find the length and width

The width $x = 7$ cm.
The length is $x + 9=7 + 9 = 16$ cm.

Answer:

Width = 7 centimeters
Length = 16 centimeters