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

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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

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