Room Width

Question

Examining the blueprints for a rectangular room that is 14 feet longer than it is wide, an electrician determines that a wire run diagonally across this room will be 26 feet long. What is the width of the room?

Answer 1

Hi Ethan,

Let the length of width be x, then the length of the long side will be x + 14

According to the Pythagorean Theorem, x^2 + (x+14)^2 = 26^2

x^2 + x^2 + 28x + 196 = 676

2x^2 + 28x - 480 = 0

divide by 2

x^2 + 14x - 240 = 0

(x + 24)(x - 10) = 0

x = 10 ft