Question

# Question 4 (v) Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: 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.

Solution

## Let length and breadth of rectangle be x unit and y unit respectively. Area = xy According to the question, (x - 5) (y + 3) = xy - 9 ⇒ 3x - 5y - 6 = 0 ... (i) (x + 3) (y + 2) = xy + 67 ⇒ 2x - 3y - 61 = 0 ... (ii) By cross multiplication, we get x305−(−18)=y−12−(−183)=19−(−10) x323=y171=119 x = 17, y = 9 Hence, the length of the rectangle = 17 units and breadth of the rectangle = 9 units

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