The length of a rectangle is increased by 15% and the width is reduced by 15%. Let us calculate the percentage increase or decrease of the area of the rectangle.
Answers
Step-by-step explanation:
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Step-by-step explanation:
Given :-
The length of a rectangle is increased by 15% and the width is reduced by 15%.
To find :-
Calculate the percentage increase or decrease of the area of the rectangle?
Solution:-
Let the length of the rectangle be L units
Let the breadth of the rectangle be B units
Area of the rectangle = Length× Breadth sq.units
=> Area of the rectangle = LB sq.units ----(1)
If the length is increased by 15% then the new length of the rectangle
=> L+15% of L
=> L + (15/100)×L
=> L+(15L/100)
=>L+(3L/20)
=> (20L+3L)/20
=> 23L/20 units
and
If the breadth is decreased by 15% then the new breadth of the rectangle
=> B-15% of B
=> B - (15/100)×B
=> B - (15B/100)
=> B - (3B/20)
=> (20B-3B)/20
=> 17B/20 units
Area of the new rectangle
=> (23L/20) × (17B/20)
=> (23L×17B)/(20×20)
=> 391LB /400
Area of the new rectangle = 391LB/400 sq.units
Area of the original rectangle > Area of the new rectangle
=> LB > (391LB/400)
Decreased in Area of the rectangle
=>Original area - New Area
=> LB - (391LB/400)
=> (400LB - 391LB)/400
=> 9LB/400
Decreased in the area of rectangle =
9LB/400 sq.units
Decreased Percentage in the area
= (Decreased area/Original area)×100
=[(9LB/400)/LB]×100
= (9LB/400LB)×100
= (9/400)×100
=(9×100)/400
= 900/400
= 9/4
= 2.25%
Decreased Percentage in the area = 2.25%
Answer :-
Decreased Percentage in the area of the rectangle is 9/4% or 2.25% or 2 1/4 %
Used formulae:-
- Area of the rectangle = Length× Breadth = lb sq.units