I assume the rug is rectangle.
The area of rectangle is width (W) multiply by hight (H)
\(A=4\frac{15}{36}=4\frac{5\cdot3}{12\cdot3}=4\frac5{12}\\\\H=2\frac34\\\\\\A=W\cdot H\\\\4\frac{5}{12}=W\cdot2\frac34\\\\4\frac5{12}:2\frac34=W\\\\ \frac{4\cdot12+5}{12}:\frac{2\cdot4+3}{4}=W\\\\ \frac{53}{12}:\frac{11}4=W\\\\ \frac{53}{12}\cdot\frac4{11}=W\\\\ \frac{53\cdot4}{3\cdot4\cdot11}=W\\\\W=\frac{53}{33}\\\\W=1\frac{20}{33}\)
The rug is \(1\frac{20}{33}\) meters wide
