The important question of Pair of linear equations in two variables chapter how i solve this question Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle. Q.4(5)
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Let,
The length of rectangle = x unit
And breadth of the rectangle = y unit
Now, as per the question given,
(x – 5) (y + 3) = xy -9
3x – 5y – 6 = 0……………………………(1)
(x + 3) (y + 2) = xy + 67
2x + 3y – 61 = 0…………………………..(2)
Using cross multiplication method, we get,
x/(305 +18) = y/(-12+183) = 1/(9+10)
x/323 = y/171 = 1/19
Therefore, x = 17 and y = 9.
Hence, the length of rectangle = 17 units
And the breadth of the rectangle = 9 units