Set up and solve a quadratic equation: The screen of a new laptop has a diagonal of 17 inches. If the length of the computer is 1 inch less than twice the width, find the dimensions of the computer.
Mathematics · High School · Thu Feb 04 2021
Answered on
considering the Pythagoras theorem
hypotenuse = length of diagonal = 17 in
base = width = x
height = L = 2x -1
then
x² + (2x - 1)² = 17²
x² + 4x² - 4x + 1 = 289
5x² -4x = 288
5x² - 4x - 288 = 0
(5x + 36 )(x - 8) = 0
We can disregard the factor (5x + 36) because dimensions cannot be negative. So we only need to solve:
x - 8 = 0
x = 8 in. the width of the monitor.
The length = 2x - 1
= 2(8) - 1
= 16 - 1
= 15 in.