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
- Let us assume the length and breadth of the rectangle be x units and y units respectively.
- 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=(y−7) units ∴ New area=(x+14)(y−7) square units∴ (x+14)(y−7)−xy=35⟹xy−7x+14y−98−xy=35⟹14y−7x=133⟹2y−x=19…(i) - 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=(x−7) unitsNew breadth=(y+3) units ∴ New area=(x−7)(y+3) square units∴ xy−(x−7)(y+3)=105⟹xy−(xy+3x−7y−21)=105⟹xy−xy−3x+7y+21=105⟹7y−3x=84…(ii) - On multiplying (i) by 3 we get:6y−3x=57…(iii) Subtracting (iii) from (ii), we get:y=27
- Putting y=27 in (i), we get:(2×27)−x=19⟹x=54−19=35
- Hence, Length=x units=35 unitsBreadth=y units=27 units