Rectangular plot

The dimensions of a rectangular plot are (x + 1) m and (2x − y) m. The sum of x and y is 3 m and the perimeter of the plot is 36 m. Find the area of the plot and the length of its diagonal.

Final Answer:

S =  64.6875 m²

Step-by-step explanation:

$$\begin{gathered} x+y=3 \\ 34=2\cdot (x+1)+2\cdot (2\cdot x-y) \\ 6x-2y=32 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ 1.33y=-2.33 \\ y=\frac{-2.33333333}{1.33333333}=-1.75 \\ x=\frac{32+2y}{6}=\frac{32+2\cdot (-1.75)}{6}=4.75 \\ x=\frac{19}{4}=4.75 \\ y=\frac{-7}{4}=-1.75 \\ a=x+1=4.75+1=\frac{23}{4}=5.75\text{m} \\ b=2\cdot x-y=2\cdot 4.75-(-1.75)=\frac{45}{4}=11.25\text{m} \\ S=a\cdot b=5.75\cdot 11.25=64.6875{\text{m}}^2 \end{gathered}$$

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