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Ishan wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot ,he told that if its lenght is decreased by 50m and breadth increased by 50m,then area will remain same but if length is decreased by 10m and breadth decreased by 20m then area will decreased by 5300 metre square. using Matrix method, find dimensions of the plot

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Answers:

Ans. Let the length of Plot = x m
Breadth of plot = y m
Area of Plot = xy
According to First condition,
(x50) (y+50) = xy
=> xy + 50x 50y  2500 = xy
=> 50x  50y = 2500
=> x y = 50 ........ (1)
According to 2nd condition,
(x10) (y20) = xy  5300
=> xy  20x  10y + 200 = xy  5300
=> 20x  10y = 5500
=> 20x + 10y = 5500
=> 2x + y = 550 ........(2)
We can represent these two equation using Matrix
A = {tex}\begin{bmatrix} 1 & 1 \\ 2& 1 \end{bmatrix}{/tex}, A = 1+2 = 3
X = {tex}\begin{bmatrix} x \\ y \end{bmatrix}{/tex}
B = {tex}\begin{bmatrix} 50 \\ 550 \end{bmatrix}{/tex}
Such that AX = B
X = A^{1}B
A^{1 }= {tex}Adjoint \space of \space A\over Determinant \space of \space A {/tex}=> X= {tex}{1\over 3} \begin{bmatrix} 1 & 1 \\ 2& 1 \end{bmatrix}\begin{bmatrix} 50 \\ 550 \end{bmatrix}{/tex}
=> X = {tex}{1\over 3}\begin{bmatrix} 600 \\ 450 \end{bmatrix}{/tex}
=>X = {tex}\begin{bmatrix} 200 \\ 150 \end{bmatrix}{/tex}
x = 200
y = 150
So Length of Plot = 200 m
Breadth of Plot = 150 m
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Ans.
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Explanation:
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Answers:

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Ans.
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Ans.
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