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

Question

Mathematics

Charlie Glover

28 August, 22:33

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

+1

Answers (1)

Know the Answer?

Yair Padilla · Answer 1

So remember that the pythagorean theorem is a^2+b^2=c^2

c=18

legnth is 3 more than width

l=3+w

a=3+b

subsitute

(3+b) ^2+b^2=18^2

expand

9+6b+b^2+b^2=324

subbtract 9 from both sides

6b+2b^2=313

subtract 313 from both sides

2b^2+6b-313=0

factor

use quadratic formula and get

b=11.1

subsitute

a=3+b

a=3+11.1

a=14.1

answer is 14.1 ft by 11.1 ft