Question

If in a rectangle, the length is increased and breadth each by 2 units, the area is readuced by 28 square units. If, however the length is reduced by 1 unit and the breadth is increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.

Answer 1

Heya ! Here is your answer ⤵⤵

$let \: the \: length \: be \: x \\ let \: the \: \: breadth \: be \: y \\ area = xy \\ \\ increasing \: l \: and \: b \: by \: 2 \\ (x + 2)(y + 2) = xy - 28 \\ decreasing \: l \: andb \: \\ (x - 1)(y + 2) = xy + 33 \\ solving \\ \\ (1)xy + 2x + 2y + 4 - xy + 28 = 0 \\ 2x + 2y + 32 = 0(1) \\ \\ (2)xy + 2x - y - 2 - xy - 33 = 0 \\ 2x - y - 35 = 0(2) \\ \\ solving \: by \: elimination \\ x + y + 16 = 0 \\ 2x - y - 35 = 0 \\ - ... + .. + \\ - x + 51 = 0 \\ x = 51units \\ y = 67units$
Hope it helps you ✌✌