Mathematics High School

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width. What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot. 10. 4 feet by 7. 4 feet 11. 1 feet by 8. 1 feet 13. 4 feet by 10. 4 feet 14. 1 feet by 11. 1 feet.

Answers

Answer 1

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

A right angle triangle has the longest side as the hypotenus which is also the diagonal.

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

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============================================

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---------

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