Question

Choose two positive integers a and b, making sure that a<5 and b>80 . The width of a rectangular computer screen is a inches more than its height. If the area of the screen is is b square inches, determine the dimensions of the computer screen.

Answer 1

Answer:

Dimensions of the screen are a minimum of 10 inches wide by 8 inches high. The difference between the height and width will be 2 inches

Step-by-step explanation:

$Height = H$

$Width = H + a$

$Area = Height x Width$

$b = H * (H + a)$

$b = H^{2} + aH$

$H^{2} + aH > 80$

$H^{2} + aH - 80 > 0$

a<5 means 'a' can be a = 1, 2, 3, 4

Solving for H for each option of 'a' will give values of 'H' using the quadratic formula below

$H = \frac{-b\±\sqrt{b^{2}-4ac}}{2a}$

As 'a' and 'b' must be positive integers, H and W must be positive integers as well,

$a = 1, H = 8.46, H = -9.46$

$a = 2, H = 8, H = -10$

$a = 3, H = 7.57, H = -10.57$

$a = 4, H = 7.17, H = -11.17$

Based on above possible answers:

$a=2, H=8$

$W = H + a$

$W = 8 + 2$

$W = 10$

Dimensions of the screen are a minimum of 10 inches wide by 8 inches high. The difference between the height and width will be 2 inches