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. However, if we decrease its length by 7 units and increase breadth by 3 units. Its area is decreased by 105 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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