computer manufacturing company would like to come up with a new laptop
computer such that its monitor is 80 a square inches smaller than the present ones.
Suppose the length of the monitor of the larger computer is 5 inches longer than
its width and the area of the smaller computer is 70 square inches. What are the
dimensions of the monitor of the larger computer?
If the larger monitor has width w, then its length is w+5. So, we have
w(w+5)-80 = 70
w^2 + 5w - 150 = 0
(w+15)(w-10) = 0
...
To find the dimensions of the monitor of the larger computer, let's assign variables to the width and length of the monitor.
Let's assume:
Width of the monitor of the larger computer = x inches
Length of the monitor of the larger computer = x + 5 inches
The area of the larger computer's monitor can be found by multiplying the width and length:
Area = Width × Length
Given that the area of the smaller computer is 70 square inches, we can set up the equation:
70 = Width (x) × Length (x + 5)
Now, we need to find the value of x. We can solve the equation for x using the given information.
Step 1: Substitute the values into the equation.
70 = x × (x + 5)
Step 2: Simplify and make the equation quadratic.
70 = x^2 + 5x
Step 3: Rearrange the equation to form a quadratic equation.
x^2 + 5x - 70 = 0
Now we can solve this quadratic equation to find the possible values for x using factoring or the quadratic formula.
Step 4: Factor the quadratic equation.
(x - 7)(x + 10) = 0
Step 5: Solve for x.
x - 7 = 0 or x + 10 = 0
x = 7 or x = -10
Since width cannot be negative, we discard x = -10.
So, the width of the monitor of the larger computer is 7 inches.
Step 6: Calculate the length of the monitor.
Length = Width + 5
Length = 7 + 5
Length = 12 inches
Therefore, the dimensions of the monitor of the larger computer are:
Width = 7 inches
Length = 12 inches
To find the dimensions of the monitor of the larger computer, we can set up an equation based on the given information.
Let's assume the width of the monitor of the larger computer is x inches. According to the given information, the length of the monitor is 5 inches longer than its width, so the length would be x + 5 inches.
The area of a rectangle can be found by multiplying its length and width. The area of the smaller computer is given as 70 square inches, so we can set up the equation:
Width * Length = Area
x * (x + 5) = 70
Now, let's solve the equation:
x^2 + 5x = 70
Rearranging the equation:
x^2 + 5x - 70 = 0
Now, we can factor the quadratic equation:
(x + 10)(x - 7) = 0
From this, we can determine that either x + 10 = 0 or x - 7 = 0.
If x + 10 = 0, we get x = -10, which is not a valid solution for the width.
If x - 7 = 0, we get x = 7, which is a valid solution for the width.
Therefore, the width of the monitor of the larger computer is 7 inches.
Since the length is 5 inches longer than the width, the length of the monitor would be 7 + 5 = 12 inches.
So, the dimensions of the monitor of the larger computer are 7 inches by 12 inches.