Example 19 The area of a rectangle gets reduced by 9 sq. units, if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, then the area is increased by 67 sq. units. Find the dimensions of the rectangle.
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Step-by-step explanation:
solution ⇒
Let length = X and Breadth = y
Area = xy
ACCORDING TO THE QUESTION
⇒( X - 5 ) (Y + 3 ) = xy - 9
⇒3X - 5Y - 6= 0
⇒(X + 3)(y + 2) = XY + 67
⇒ 2X - 3Y - 61= 0
BY CROSS MULTIPLICATION
⇒Y/305 - ( -18) = y/-12 + 183
⇒X/323 = Y/171= 1/19
⇒X = 17 ⇌ Y = 9
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