the length of a rectangle is increased by 60% . By what percent would the breadth the decrease to maintain the same area.
Answers
Answer:
percentage of breadth is decreased by 37.5%
Answer :
- The breadth of a rectangle is decreased by 37.5%
Given :
- The length of a rectangle increased by 60%
To find :
- By what percent would the breadth the decrease to maintain same area
Solution :
To find the area we have to take the original length be 100 and also original breadth be 100 then after length is increasing as given in question and breadth is decreasing of x then after to find the new area which is equal to the original area then to find the value of x (breadth)
- Let the length of rectangle be 100
- Let the breadth of rectangle be 100
As we know that
- Area of rectangle = length × breadth
➞ Area of rectangle = 100 × 100
➞ Area of rectangle = 10000 m²
According to question, Given that the length of a rectangle is increased by 60% so ,
Finding the new length area :
To find the new length we have to find the length of 60% then we have to add it to the original length
➞ 100 + 60% of 100
➞ 100 + 60/100 × 100
➞ 160m
New length is 160m.
Let us assume that the breadth is decreasing at the x%
Finding the new breadth area :
To find the new breadth ,We have to find the x% of length then we have to subtract it to the original breadth
➞ 100 + x% of 100
➞ 100 - x/100 × 100
➞ (100 - x)m
New breadth is (100 - x)m
- New length and breadth area = 160 × (100 - x)
Finding the breadth of rectangle is decreased by?
Given that, area should be same so,
- New length and breadth area = Area of rectangle
➞ 160 × (100 - x) = 10000
➞ (100 - x) = 10000/160
➞ x = 100 - 125/2
➞ x = 100 - 62.5
➞ x = 37.5 %
Hence , The breadth of a rectangle is decreased by 37.5%