If the length of a rectangle is increased by 1414 units and its breadth is decreased by 77 units then the area of the rectangle is increased by 3535 square units. However, if we decrease its length by 77 units and increase breadth by 33 units. Its area is decreased by 105105 square units. Find the length and breadth of the rectangle.


Answer:

Length=35 unitsBreadth=27 units

Step by Step Explanation:
  1. Let us assume the length and breadth of the rectangle be x units and y units respectively.
  2. It is given that if the length of a rectangle is increased by 14 units and its breadth is decreased by 7 units then the area of the rectangle is increased by 35 square units.
    Now, New length=(x+14) unitsNew breadth=(y7) units  New area=(x+14)(y7) square units (x+14)(y7)xy=35xy7x+14y98xy=3514y7x=1332yx=19(i)
  3. Similarly, if we decrease its length by 7 units and increase breadth by 3 units. Its area is decreased by 105 square units.
    Now, New length=(x7) unitsNew breadth=(y+3) units  New area=(x7)(y+3) square units xy(x7)(y+3)=105xy(xy+3x7y21)=105xyxy3x+7y+21=1057y3x=84(ii)
  4. On multiplying (i) by 3 we get:6y3x=57(iii) Subtracting (iii) from (ii), we get:y=27
  5. Putting y=27 in (i), we get:(2×27)x=19x=5419=35
  6. Hence, Length=x units=35 unitsBreadth=y units=27 units

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