Area Problems
The length of a rectangle room is 4 meters . if it can be partitioned into two equal square rooms . what is the length of each partition in meters?
Let the width of the room be x membersThen, its area = (4x) m2Area of each new square room = (2x)m2Let the side of each new room = y metersThen, y2 = 2xClearly, 2x is a complete square when x=2? y2 = 4? y = 2 m .
Let the side of the square = 100 m So area of square = 100 x 100 = 10000.New length = 140 m, New breadth = 130 mIncrease in area = [(140 x 130) - (100 x 100)] m2= 8200 m2? Required increase percent = (8200/ 10000) x 100 % = 82%
Let circumference = 100 cm . Then, ? 2?r = 100? r = 100/2? =50/?? New circumference = 105 cm Then, 2?R = 105? R = 105 / (2?)&rArr Original area = [ ? x (50/?) x (50/?) ] = 2500/? cm2? New Area = [? x (105/2?) x (105/2?)]= 11025 / (4?) cm2? Increase in area = [11025/(4?)] - 2500/? cm2= 1025 / 4? cm2Required increase percent [1025/(4?)] x 2500/? x 100 = 41/4%= 10.25%
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