Question

A computer company makes a rectangular screen with a The dimensions of the computer screen are modeled by diagonal of 20 inches. The width of the screen is 4 inches less than its length. the equation x (x 4) 20. What is the value of x, the length of the screen? Ox-16 O X12 Ox 12 O x 16 20 in. (x-4) in. Xin. Not drawn to scale​

Answer 1

Answer:

  x = 16

Step-by-step explanation:

The equation shown can be solved this way.

  x^2 +(x -4)^2 = 20^2

  x^2 +x^2 -8x +16 = 400

  2x^2 -8x -384 = 0

  x^2 -4x -192 = 0

  (x -16)(x +12) = 0

The positive solution is ...

  x = 16

_____

Since this makes use of the Pythagorean theorem, you've probably run across the 3-4-5 triangle. You often find scaled versions of it in algebra and geometry problems. Here, it is scaled by a factor of 4 to give a 12-16-20 triangle as half of the display screen.

The 3-4-5 triple is the only Pythagorean triple that is an arithmetic sequence. So, if the difference in side lengths is 4 and the diagonal is 5×4, you can be pretty certain that x = 4×4 and x-4 = 4×3.