The area of a rectangle goes down by 9 square units when its length is reduced by 5 units and its breadth increased by 3 units. If instead the length is increased by 3 units and the breadth by 2 units, the area goes up by 67 square units. Find the length of the rectangle.

Question

Accepted Answer

17 units. Let the length be x and the breadth y. (x - 5)(y + 3) = xy - 9 expands to 3x - 5y = 6. (x + 3)(y + 2) = xy + 67 expands to 2x + 3y = 61. Multiplying the first by 3 and the second by 5: 9x - 15y = 18 and 10x + 15y = 305. Adding: 19x = 323, so x = 17 and y = 9. Check: 17 x 9 = 153; 12 x 12 = 144 = 153 - 9, and 20 x 11 = 220 = 153 + 67. 9 units is the breadth; 12 units is the reduced length and 20 units the increased length, neither of which is the rectangle's own length.

The area of a rectangle goes down by 9 square units when its length is reduced by 5 units and its breadth increased by 3 units. If instead the length is increased by 3 units and the breadth by 2 units, the area goes up by 67 square units. Find the length of the rectangle.

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