An oriental rug is 3 feet longer than it is wide. If the diagonal of the rug is 12 feet, find its dimensions to the nearest tenth of a foot.

Question

I have tried everything and I can not figure out this question. I do not know how to do this. I have tired and I keep getting it wrong.

Answer 1

The answer is 6.9ft×9.9ft ( 6.8516465442 ~6.9).

 

So the width is X and the length is X+3 (since is 3 ft longer). The hypotenuse (diagonal) is 12 ft

 Use Pythagorean theorem a^2+b^2=c^2 where as x^2+ (x+3)^2=12^2 solve it and you'll get 2x^2+6x+9=144. Move 144 to the left side so the right side is zero. 2x^2+6x-135=0. Now use quadratic formula (x=[-b ±square root(b^2-4ac)/2a] you should get either x= 6.8516465442 or -9.8516465442. Since the length can't be negative then is has to be the 6.9 answer. X=6.9ft for width and x+3= 9.9. Hope this helps!