if all sides of a rectangle is increased by 40% then, by what percentage does its area increased
Answers
GIVEN :-
- All sides of Rectangle is increased by 40%.
TO FIND :-
- Percentage by which the area is increased.
SOLUTION :-
Let the Initial length and breadth of the rectangle be 'l' and 'b' respectively.
Original Area = l × b
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Now , all the sides are increased by 40%.
♦ New length
= l + 40% of l
= l + (40/100) × l
= l + (4l/10)
= 14l/10
♦ New breadth
= b + 40% of b
= b + (40/100) × b
= b + (4b/10)
= 14b/10
New Area = (14l/10) × (14b/10)
New Area = 196lb/100
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% increase =
[(New area - Original area)/Original area] × 100
= {(196lb/100) - lb}/lb] × 100
= {(196lb - 100lb)/100}/lb] × 100
= {(96lb/100)/lb} × 100
= (96/100) × 100
= 96%
Hence , area is increased by 96%.
MORE TO KNOW :-
★ Area of triangle = (1/2) × b × h
★ Area of square = side²
★ Area of parallelogram = b × h
★ Area of trapezium = (sum of parallel sides/2) × h
★ Area of circle = πr²
Answer
hence the answer is 96%
