Answer :
Answer:
Length = 11.59 in
Width = 8.59 in
Explanation:
To calculate the length and width of the screen, we need to look at the information given to us. Since they do not give us actual values, we can assume that is the width is x, and since the length is 3 in. more than the width, the length is x+3.
It is also given that if the length is doubled ( 2(x+3) ), and the width is decreased by 1 in. ( (x-1) ), then the area would be 176 in².
Since we know area is equal to length multiplied by width, we can assume:
2(x+3) * (x-1) = 176
which can be simplified to
x² + 2x - 91 = 0
using the quadratic formula to solve for x, we find that
x = 8.59 in and x = -10.59 in
Knowing that we cannot have negative distance, we take that x = 8.59 in.
This would mean that the length of the screen would be (8.59+3), which is 11.59 in, and the width would be 8.59 in.
Final answer:
The dimensions of the monitor screen can be found by setting up an equation with the width represented as w and the length as w+3. The changes described in the problem lead us to a quadratic equation w^2 - w - 182 = 0, which upon solving gives the original dimensions of the monitor screen.
Explanation:
To solve for the dimensions of the monitor screen, we can use variables to represent the unknown length and width, and set up an equation based on the problem's description. Let's denote the width as w and, accordingly, the length as w+3 (since the length is 3 in. more than its width). After making the changes as mentioned in the problem (doubling the length and decreasing the width by 1 in.), the new dimensions become 2(w+3) for the length and w-1 for the width.
The original area of the monitor screen is w(w+3). The problem states that after the modifications, the area is increased by 176 sq in. So, the increased area is w(w+3) + 176. The new area can also be expressed as (2(w+3))(w-1). Equating these expressions and solving for w gives us the original width, and we can find the length by adding 3 to the width.
The equation to solve is therefore w(w+3) + 176 = (2(w+3))(w-1). Expanding and simplifying, we get w^2 + 3w + 176 = 2w^2 + 4w - 2w - 6, which simplifies to w^2 - w - 182 = 0. Solving this quadratic equation gives us two possible values for w, but we discard the negative value since dimensions cannot be negative. This gives us the width, and consequently, the length of the screen.
