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Pair of Linear Equations in Two Variables
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28/05/2021 10:27 am
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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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28/05/2021 10:29 am
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 breadth of the rectangle = 9 units