Q42 of 44 Page 4

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 length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by Using matrices, find the dimensions of the plot. Also, give a reason why he wants to donate the plot for a school.(CBSE 2016)

let the length be x and breadth be y

For the first condition


(x - 50) (y + 50) = xy


50x – 50y = 2500


x – y = 50 …. (i)


For the second condition


(x - 10) (y - 20) = xy – 5300


2x + y = 550 …(ii)


Substituting these values in matric form



It is in the form of AX = B, then the solution matric is X = A - 1X



|A| = 1 + 2 = 3





Therefore, x = 200 and y = 150

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