Question

Solve the problem. Check answers to be sure they are reasonable.

x + 3 The dimensions of a rectangular monitor screen are such that its length is 3 in. more than its width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 266 in. What are the length and width of the screen? The length of the monitor screen is and the width is. Enter your answer in the edit fields and then click Check Answer.

Answer 1

To find the dimensions of the monitor screen, we set up an equation using the given conditions, solve the resulting quadratic equation, and check that the solutions are positive and reasonable.

Step-by-step explanation:

To solve the problem involving the dimensions of a rectangular monitor screen, we let x represent the width of the monitor screen. We are then told that the length is x + 3 inches. When the length is doubled, it becomes 2(x + 3), and when the width is decreased by 1 inch, it becomes x - 1 inches. The problem states that this change in dimensions results in an increase of 266 square inches in the area of the screen.

We can write an equation for the change in area:
original area + 266 = new area, which translates to:
(x)(x + 3) + 266 = (2(x + 3))(x - 1)
By simplifying and solving the quadratic equation, we can find the original dimensions of the screen. Checking the solutions for reasonableness ensures that we only consider positive dimensions, as negative dimensions are not possible for physical objects.