Rectangular plot

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

Result

S =  64.688 m2

Solution:

 x+y=3 34=2 (x+1)+2 (2 xy)  x+y=3 6x2y=32  x=194=4.75 y=74=1.75  a=x+1=4.75+1=234=5.75 m b=2 xy=2 4.75(1.75)=454=11.25 m  S=a b=5.75 11.25=103516=64.6875=64.688 m2 \ \\ x+y = 3 \ \\ 34 = 2 \cdot \ (x+1) + 2 \cdot \ (2 \cdot \ x-y) \ \\ \ \\ x+y = 3 \ \\ 6x-2y = 32 \ \\ \ \\ x = \dfrac{ 19 }{ 4 } = 4.75 \ \\ y = \dfrac{ -7 }{ 4 } = -1.75 \ \\ \ \\ a = x+1 = 4.75+1 = \dfrac{ 23 }{ 4 } = 5.75 \ m \ \\ b = 2 \cdot \ x-y = 2 \cdot \ 4.75-(-1.75) = \dfrac{ 45 }{ 4 } = 11.25 \ m \ \\ \ \\ S = a \cdot \ b = 5.75 \cdot \ 11.25 = \dfrac{ 1035 }{ 16 } = 64.6875 = 64.688 \ m^2



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