A rectangular rug divided by its diagonal becomes a right angle triangle
The length and width of the rug is 14.1 feet by 11.1 feet
Diagonal = 18 feet
width = x
length = x + 3
diagonal ² = length ² + width ²
18² = x² + (x + 3)²
18² = x² + x² + 6x + 9
324 = 2x² + 6x + 9
2x² + 6x + 9 - 324 = 0
2x² + 6x - 315 = 0
solve using quadratic formula
x = - b ± √b² - 4ac / 2a
= - 6 ± √6² - 4×2×-315 / 2×2
= -6 ± √36 - (-2520) / 4
= -6 ± √36 + 2520/4
= -6 ± √2556 / 4
= - 6 ± 6√71 / 4
= -6/4 ± 6√71 / 4
= -3/2 ± 3√71/2
x = 11.1392 or -14.1392
The value of x can't be negative
So,
x = 11.1 to the nearest tenth
Therefore, the value of width and length is
width = x
= 11.1 feet
length = x + 3
= 11.1 + 3
= 14.1 feet
Learn more about Pythagoras theorem:
https://brainly.com/question/20545047
