Question

The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?

Answer 1

1. The problem says that the television has a rectangular shape. So, the formula for caculate the area of a rectangle is:

 A=LxW

 "A" is the area of the rectangle (A=3456 inches²).
 "L" is the the length of the rectangle.
 "W" is the width of the rectangle.

 2. The width of the screen is 24 inches longer than the length. This can be expressed as below:

 W=24+L

 3. Then, you must substitute W=24+L into the formula A=LxW:

 A=LxW
 3456=L(24+L)
 3456=24L+L²

 4. The quadratic equation is:

 L²+24L-3456=0

 5. When you solve the quadratic equation, you obtain:

 L=48 inches

 6. Finally, you must substitute the value of the length, into W=24+L:

 W=24+L
 W=24+48
 W=72 inches

 7. Therefore, the dimensions of the screen are:

 L=48 inches
 W=72 inches