There is a square of $x$ units length and a rectangle of $x$ units length and $y$ units breadth. Express the difference in the perimeter of the two figures using an algebraic expression.

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Solution

Forming an algebraic expression:
The length of square $= x$ units
The perimeter of a square $= 4 \times s i d e = 4 x$
The length of rectangle $= x$ units
The breadth of rectangle $= y$ units
The perimeter of a rectangle $= 2 (l e n g t h + b r e a d t h) = 2 (x + y)$
The difference in the perimeter of the two figures $= 4 x - 2 (x + y)$
Thus, the difference in the perimeter of the two figures is $4 x - 2 (x + y)$ .

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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. However, if the length of this rectangle increases 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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According to first condition :
$(x - 5) (y + 3) = x y - 9$ and